A vigorously growing rootstock doesn't normally kill the scion, it just gradually takes over. Your true lemon sounds in a bad state - flowers growing on bare stems is a last ditch effort by the plant at reproduction. Are you sure there's nothing else wrong with the grafted lemon? Look carefully at the stem and see if there's a problem there - dying, rotting or damaged in some way.
If you think there's a chance of the smoothskin lemon recovering, I would cut back nearly all the rootstock growth, perhaps leaving just two or three nodes on a remaining stem so that you have a chance of re-growing the rootstock variety once the other one has recovered. Hard pruning of a vigorous rootstock won't do any harm, although you will probably miss a years fruit on that section.

thank you for your advice, I'll inspect the stem in the morning. I haven't noticed anything strange about it though, but stand to be corrected. several of the small branches have died back, which might be an ominous sign. I'll take some pics, but not sure that they will help. At least, no sign of any insect/fungus activity that I could ID. The smoothskin's trunk is thicker and coarser looking than that of the rootstock, but I think that has always been the case with this tree.
Do you agree that I should remove all the fruit left? perhaps also all the baby lemons on the rootstock (could it be 'sucking' the life out of the rest of the tree?)
I would be devastated if I killed the entire tree!. It has been happily doing its own thing since we moved here, 5 years ago, so haven't really paid too much attention to it. it has various herbs and things growing under it (basil, chillies, lemongrass, mint, celery), and has had for several years, the only new addition being lemon balm (very small), which I doubt is of any significance. Only once I noticed that the grafted part was looking bad and the rootstock's leaves were a bit yellow, did I add some epsom salts, not a lot, and I have not noticed any change in the true lemon since then, so do not think it had any influence on the current situation.
If the poor plant is doing its best to reproduce, should i maybe remove both fruit and buds, hopefully encouraging it to make some leaves? And what about pruning the non-fruit or leaf-bearing branches? surely they are sucking life out with no return? My other lemon (a peculiar, very large, oval, thick-skinned and not very sour with quite dry but tasty flesh)also has some of these dead-end branches, but is doing fine, by the looks of it
thanks again,
karen

prune back all the root stock that is growing leaves. Prune it back to where the original graft is and keep all new growth cut off from the place where you cut back. In other words, only let the good grafted part grow. I think you will see restored vigor very soon.

thanks for your advice too, softmentor.
I have looked at the stem of the smooth one, and noticed that quite a bit of the bark is loose in places, can be pulled off easily, and is definitely dead, with some white fluffy spiders-nesty looking spots underneath. I will definitely take a pic as soon as I get a chance and post it.
Now I am a bit afraid of cutting all the rootstock down in case the other one has some disease or is dying from who knows what. Then I'll have lost both!

I have finally managed to take some pics of the stem of the grafted part of the lemon. Due to this worrying condition, I have put off removing more of the healthy rootstock part, as mentioned before.
figuring out how to post the pics, however, proved to be quite a challenge.
I hope I get it right:

Did you have a hard freeze this past summer (your winter)? That looks like it either had a hard freeze or is deseased. Either way I don't think it will survive. The scion that is (part above the rootstock). Unless there is a part of the scion below what your pictures shows. If it is freeze damage just let the rootstock grow and use the fruit. If it is deseased you may be better off removing the whole tree rootstock and all.

Thank you for your comments. The part below what the picture shows looks pretty much the same, I'm afraid.
I'm not too sure what a hard freeze is! We do not get snow here (only very rarely on top of the mountain), but have had a particularly cold winter, with several episodes of hail. I can't seem to find past temp. data at the moment, but I doubt whether it ever went below 0C, as that would be very unusual. Nevertheless, I think it has been one of our coldest and longest winters in a long time, so perhaps that might have had some impact.
If it is diseased, shouldn't the rootstock also be showing symptoms?
I have a terrible habit of getting attached to my plants (I'm sure I'm not the only one!), so am holding thumbs that it might recover.
What are the most common citrus diseases that would cause this kind of reaction?

Rootstock frequently are tolerant of most citrus deseases. That is one of the reasons they are selected for use as a rootstock. Being tolerant the rootstock can be infected without showing symptoms. With some deseases that tolerance can be passed on to the scion. But with some deseases that are external infections such as phytopthera that tolerance is not passed on. The reason I say that if it is indeed deseased that you should remove the whole tree is the fact that the rootstock can act as a reservoir of the desease that may be spread to other citrus. Here is a link to a good site on citrus pests. There are many of the deseases of citrus(not all) listed. Look more closely at the link for 'phytopthera gummosis'. Notice that it says that the sap may not be present only because it could have been washed of by rain.
BTW is holding thumbs kinda like crossing fingers? ;^)

Here is a link that might be useful: Citrus pests

Thank you Citrusenthusiast, funny you should say that about phytopthera - I am also in the throes of despair about one of my chile plants that went from fine to completely wilted (and now pulled out) overnight. The most likely reason is indeed Phytopthera, as far as I can gather from what I've read (am on the hot chile forum about this as well). But it seems to be a slightly different strain/species of Phytopt. than the one you mention, but I'm not sure. Someone on the pepper forum also suggested Pythium, which I am now researching.
I haven't noticed sap leaking from the bark, but I certainly wasn't looking for it either. We have had a very wet winter, and now, although it is supposed to be summer, we are having some rainstorms as I type. This does not bode well for anything infected with Phytopthera, as far as I can gather.
Looks like I'll have to try the bark removal with lesoin burning as well as some copper spray, as recommended on that site - thanks for the link, it is very informative.
I have 2 more citrus trees in my very small garden, one a newly acquired Tahiti lime, and the other a rather strange very large, very thick pithed(?) one. My paranoia of cross-infection is growing by the minute!
I am also staring to wonder whether this disease has not been lurking in the garden for a while... Last year I was away for quite a while during summer and when I returned all my tomatoes were looking dreadful, all leaves wilted but fruit still on. I first assumed that the person taking care of the garden might not have done such a good job, and then wondered whether that is the natural way once tomatoes have done their thing. Now I'm thinking that it looked suspiciously like what just happened to my one chile plant. I'm sure it's clear that I am still very new to veggie and fruit gardening, and I guess the very cramped urban space is not helping (think I might have a few too many plants in here).
I'm not doing very well at posting single pictures, so think that if you click on the link in my previous post and look around, you can also see my sadly departed chile, if interested. (think the subalbum chile plants shows closer views of the damage)

And yes, holding thumbs is the equivalent of crossing fingers, as far as I know. Think it comes from the Afrikaans which would have come from the Dutch - 'hou duimvas'.
thanks again for your advice, it is much appreciated.