Hi Tim. Thank you for using Ask Extension.  It is fun to start your own plants from seed.  You can prune as needed to maintain your tree’s shape, most lemon trees need little pruning.  Small tree shoots at the base of your lemon tree or new strange looking branches growing low on the trunk are most likely lemon tree suckers growth. Clip these and in the future any branches that are too long, and remove any growing toward the trunk of the tree instead of away from it. The suckers are the only ones that I would take off at this time.

As for rooting cuttings from a lemon tree, most lemon trees are made from grafting fruit bearing branches to dwarf or a more hardy resistant rootstock.  Semi-hardwood cuttings can be taken from late spring to early summer when a tree is in active growth and propagated.

For more info try https://ousearch.omniupdate.com/texis/search/redir.html?query=Lemon+tree&pr=uada&prox=page&rorder=500&rprox=750&rdfreq=500&rwfreq=750&rlead=750&rdepth=31&sufs=1&order=r&uq=&u=https%3A//www.uaex.uada.edu/yard-garden/in-the-garden/reference-desk/fruits/lemon.aspx&redirKey=3758a79b5979c34a8762da206edf03a84276c6d0&link
 
I wish you luck in caring for your plant.

Good luck.

Sharon

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