Starting a tree from seed is not advisable as the fruit will usually differ greatly from the parent plants, and it will be 9 or 10 years before it bears. Unless you live in zone 9 or 10, you'll need to plant your tree in a pot and move it indoors during cold weather.
Lemons have the lowest heat requirement of all citrus.
Dormant lemon trees can withstand temperatures as low as 26 degrees, but small fruit will be injured by as little as a half hour at 29 degrees. Drainage is very important to all citrus. Make sure your soil is very well draining. Lemons require full sun, at least 6 hours a day. Plant in early spring, preferably on a cloudy day to reduce shock.