Growing most types of fruit from seed is generally a bad idea. There is a high chance the fruit will not be as good as the parent variety. For those of you who are not aware of how this works, in nature fruit species can have a lot of genetic diversity from generation to generation. When a good producing tree is found, it then gets propagated from cuttings. People usually do not want to take the trouble of growing a fruit tree from seed when they do not even know whether the fruit will be good. Generally though, lemons produce truer to seed than oranges do. Not talking about citrus here, but for fruit trees in general, it is theoretically possible to breed fruit that produces truer to seed, but it takes many more generations of breeding. These are often traditional heirloom varieties that have been around a long time. Whereas the seed from a Navel orange will not really result in a Navel variety, some of these heirloom varieties can essentially be continually propagated from seed. The terms "heirloom", "true to seed", and fruit "variety" can all be very relative and ambiguous terms.

The picture that Steve circled, that scion is still alive (as you can see a fruit bloom on that branch that is cut). The other picture, the scion definitely appears dead, it may even have been killed by the tape that was used to keep it on the support having cut into the bark as the scion grew. Any of the long shoots that are trifolate (three leave - like a club playing card), like is showing on the ground in the first picture and on the tree, need to be cut as Steve mentioned. For the second tree pictured, if you don't have any leaves that are not trifolate, then you're not going to get any wanted fruit, unless you want to try grafting from your other plant.

peppystud, there are very many types of lemon trees. However, the two most common in ground planted lemons, by a very wide margin, are either Eureka or Lisbon. I would be very surprised if someone planted a different variety. Dwarf has nothing to do with variety, it has only to do with the type of root stock.

Did your trees receive adequate water this year? Were any lawn fertilizers applied near the tree? Was the tree mulched to reduce water evaporation?