Some more pics, hope it helps.

I would probably take that plant right out of the. Citrus don't like to share nutrients, water and root space.

Your tree looks dry or lacking in moisture. Have you ever let it dry out too much before? If just once then lot's of roots have passed and you need to watch your watering practices now.

If your tree was taking up moisture correctly, it should be fine in the hot sun as long as that pot is not over heating..Have you ever felt the side of that pot in the full sun? I know that dark porclean can get very hot and cook your roots. Have you tried using aluminum foil or a light colored cloth of some sort wrapped around the pot?
You could also use the pot in pot method.

Have you checked to see whether bugs are sucking the moisture out of your leaves?

Have you been watering so as to flow out from the bottom since you are fertilizing?

What kind of mix are you using and how often do you have to water? Is it porous or hard like?

That other plant tells me that something is wrong with your citrus roots since that plant is so healthy looking.

Check the roots out and do a few corrections and see what happens and welcome from across the pond!

MIke

I would remove the plant growing in your lemon tree pot. If you want to keep the plant repot it in another pot. Is there anyway you can wash your plant , it is probably full of dust and where there is dust there is usually spider mites. You will probably lose quite a few leaves if you wash , it looks like a few of the leaves are hanging on by a thread. Is there any way you can give your tree fresh air , maybe opening a window at night , I know it gets really hot in Dubai. I would definitely follow Mikes check list.

Brian

Your vine looks kind of like a pea of some kind.

I agree, pull it out. It is only going to compete with your Citrus. Also, you might wanna consider lightly pruning your tree. Your tree doesn't look too healthy and I think the trim could help it.

I also wanna add, daily misting the leaves with a spray bottle can help. CItrus like misting. What do you have for potting mix?

If you decide to prune, basically you want to take off anything that looks deformed, broken, and diseased. Then have all the growth uniform. If one branch is scraggly or growing more vigorous than the rest, cut it back to the same level as the rest of the tree growth. It may sound scary to do this but your tree will respond well to it. It will put out new healthy growth and perhaps fruit.

Citrus do not need to be misted. In fact, constant dampness can cause issues. Not sure where this misting information has come from, as it's simply not true, and unnecessary for citrus. Now, a good rinsing every now and then, to rinse off dust is a good idea, but citrus are not plants that need nor require high humidity. If that were the case, we'd never be able to grow them in S. California, especially in our deserts.

And, not sure the tree needs to be pruned, either. It does appear to be either suffering from dry soil, or possibly overly-wet/compacted soil, as the leaves look a little droopy. Once the soil and water retention/or hydrophobic soil has been addressed, I would provide regular fertilizing, and more light. With those things, you'll have more leaves sprout from the leaf nods, and your sparse canopy should fill out. And, the "hitchiker" plant should be removed.

Patty S.