Hi there Ginabarnes and all,
You can grow lemon trees easily from seed, but they take a long time to get to the stage when they produce fruit. I would go for knocking your piggy bank around and buying a young but established and fruiting tree. But then, I am impatient when it comes to lemon trees!
Seeds, if correctly planted, will take about 4+ weeks to sprout. Remove seeds from a good organic lemon; dry them off with kitchen paper or towel, then put them into a glass of tepid water and leave them overnight. Any seeds that float to the top are not likely to germinate so throw them away.
Take them out of the water and dry them and rub off the outer coat of the seed – be careful not to damage the seed. It should come off easily after the soaking, but if it doesn’t you can soak it some more OR nick it with a knife and try to peel away the hard cover.
Plant your seed in moist compost in a yoghurt container or similar at this stage. Poke holes in the soil with your finger or a dibber and cover the seed with compost, do not press down.
Keep it is a warm and sunny place and you should get results as I say within 4 to 6 weeks. Let them grow to around 4 inches high, and then you can transplant them into their pot. Plant quite a few so that in the end you will choose the strongest one for your final pot.
Keep the compost moist (not wet) and warm all the time, do not overwater or your seed might rot. I use a spray bottle to water any seeds I am growing so that I do not displace them.
Choose a deep final pot – lemon roots are long.
Finally go here to read this article which you may also find useful,
Grow a Lemon Tree Cheers now
