Frank,

There are a few keys to cultivating citrus:
Lots of light -- citrus like high light, but while it is a seedling I wouldn't set it outside in direct hot sun all day - it would probably dry out quickly. Either indoors in full sun, or partial shade outdoors until it gets a little bigger.

Well draining soil. Do a search on this forum or elsewhere and you can find some of the recommendations for potting mixes. Usuall some soil, but mostly bark, perlite, and sand are common. Citrus don't like wet roots.

Don't over-water. Let the plant dry out considerably between waterings.

When it gets a little larger fertilize with either citrus fertilizer, or with a fertilizer for acid loving plants (MiracleGro for Azaleas, for example). Citrus also require trace amounts of some other elements (micro nutrients) which are trace elements that will be in the citrus fertilizer, but not in standard fertilizers so if you can get citrus fert. go with that. Be careful not to burn the roots so fertilize extra lightly while it is small.

Also you should be aware that citrus grown from seeds will experience a fairly long period of juvenility. What this means is that for many years the plant will have very long thorns and will not flower or produce fruit. How long it stays a juvenile depends on the conditions and what citrus variety it is. It can be anywhere from 3 years up to as much as 20 years for some grapefruit varieties.

Its fun to grow from seed, but if you'd like fruit faster (and less thorns), consider buying a grafted tree (usually $20 - $40) from a local or mail-order nursery. These trees will produce plenty of fruit within 1-3 years.

Also for planting in the yard you don't mention your zone or climate. Just make sure you're somewhere suitable for growing lemons outdoors. They're not the most cold sensitive but will be killed by hard freezes.

Best of luck with your new tree (which may end up becoming treeS if you're like most of us who get into growing citrus!).

All the best,

Pelham