I just bought a Eureka lemon tree. It is in a one gallon container but it looks more like a bush than a tree. It is about three feet from the bottom of the pot to the top of the branches. Does this mean it will be a small tree like a bush and is it better to be a bush or a tree? Is the bush going to produce smaller lemons than a tree? If it is a tree at what length does it need to be cut at the trunk in order to produce more branches?
The size just means it is a young tree. Full sized trees are much more expensive to buy, because the nursery has to grow them for several more years till they reach full size, and transporting and planting a large tree isn't a simple task either. The roots also grow in proportion to what is above ground, so you have to transport a huge ball of soil, and dig a very big planting hole.
Big trees also need more substantial stakes to stop them blowing down until their roots get established, and in hot dry climates they may need lots of watering for up to a year after transplanting them.
According to one UK supplier, a fully grown Eureka lemon will be about 10 feet tall and 6 feet diameter. A US website said 20 feet tall. Your choice which to believe!
You can also grow these trees permanently in a container (but a bigger one than the one you bought it in!) in which case you would probably want to keep it pruned to something like its current size.
A young tree may not produce any fruit at all for the first years of its life. A small tree will produce fewer lemons, but not smaller ones.
If seems they don't need any special pruning. Just cut out any dead or weak-growing wood, and any branches which are rubbing against each other (because the damaged bark can allow pests and diseases to develop), and trim the tree to the shape you like. The best time for pruning is in spring when the tree is just starting to grow again after winter.
You can prune the lower branches as the tree gets taller if you like, but don't rush into doing any pruning till you have seen how it is going to develop. It will probably take another 10 or 20 years to get to its full size. The shock of being moved will slow down its growth in the first year, as well.