I have planted seeds of a lemon and want to know, if I have to graft the lemon plant so I can get lemons? Or will they in time grow without grafting?
Strictly speaking something like a sour orange is possible. A lot of things are possible really. Citrus hybridization can get very complicated. There are four 'parent species' of citrus (Citron, Pomelo, Papeda and Mandarin). A lemon is a cross between a Citron and a Sour Orange (which is itself a cross of a Mandarin and a Pomelo). So that's 3 parent species in two generations to produce the lemon you got your seed from, which only accounts for the female parent of the tree in your yard. The male part (pollen) could have come from any number of other citrus trees that flower around the same time.
So, your tree will definitely produce some manner of citrus fruit, but what that fruit will be is anyone's guess. If you want something specific, a graft would be necessary.
John McPhee wrote a very witty book on oranges, entitled, not surprisingly, 'Oranges'. One chapter recounts an effort to grow limes from seed, due to the pervasive presence of a virus in existing trees. Essentially, they grew hundreds of seedlings from limes, and got a tiny number of plants that grew limes. All the others produced some other citrus fruit. So, you can look forward to almost anything except a conventional lemon.
I planted sprouting seeds from our lemon tree about four years ago. I kept one and gave the other one to a friend. My tree is now about 8 ft. tall and is planted in our back yard. No fruit as yet but I'm hoping to see some blooms soon! The tree I gave to my friend is also doing well but like mine ...no blooms yet. The tree we have in the front yard that I got the seeds from gives us fruit you wouldn't believe! Lemons bigger than grapefruit that makes the best lemonade ever! We live in Arizona so the trees get plenty of sunshine. We also have orange trees in the back yard so maybe when my lemon tree starts to bear fruit I'll get lemoranges!!
The existing, great answers here about the fruit lotto (or Russian roulette) that one wins or loses when they grow from seed without grafting can only be added to minimally by my own examples of outcome, which were surprising and rewarding to me even having known about improbable success etc. While I've had parents or neighbors with useless bitter orange, and all my raw citrus is thorny, I have had three elements of extreme success.
1) A lucky hit of my favorite tree yielding yummy, prolific, plump oranges that is blessed not only with fruit causing people ask for cuttings off its branches to graft on to their own bases, but it is blessed with a decent-sized (if not smallish but sturdy) hearty structure and a drought and disease-resistant system which has survived all commercial varieties, now standing alone. Some areas even restrict sale or even planting of unapproved species because they want citrus in the area to be known to resist local blights, but I seem to have their regulated species beat. I keep a watchful eye out and destroy sick citrus with fire.
2) The other one (and I mourn its loss in a construction misunderstanding) was a weird, yellow fruit that looked like a lumpy, grapefruit-sized lemon. The peel was impractically thick, but they were interesting-looking and the lemony inside tasted delicious and I couldn't get over the notion they "made me feel good" enhancing my hydration with nutrients exceeding a simple ascorbic acid pill. I'd welcome another.
3) I'll also note that calamondin always seems to yield come kind of acceptable passing-for-calamondin fruit good for preserves and drinks (if not with minor variations in size, tartness, and peel-ability I've never known if was genetic or individual phenotype / environment influenced).
-- Jeff (the lay observer of what's in his yard & who was obsessed with planting saved seeds one year).
P.S. Citrus is very water and nutrient hungry, gets miserable-looking and sick without care, and makes for an inevitably sad and depressing item to just let fend for itself in every case unless one is very fortunate by chance. They don't like to come back from poor health easily and all too often, if combined, poor state + some diseases = forget it, even though it looked salvageable. In fact combining random genes with neglect can more easily cause them to spread detrimental diseases to local crops when haphazardly planted and neglected, unfortunately.
Water, pruning canopy to give roots a break, and even watered-in or diluted urine can go a long way. The best grapefruit in two come from the one the high school football team pees on each season (the elderly lady waters in the pee after practice so it doesn't sit concentrated). She says they're not technically organic or steroid free, "It's all the natural testosterone makes the fruit grow", LOL.
Native lemon trees are grown here. They are short bushy trees that produce small green lemons unless they get lots of sun, being very sour and thick skinned. Lemon trees are grown as a ornamental trees in some yards and they are normally planted where a person wants a tree about 6 feet in high. They are used as root stock for grafting other lemon trees, so what type of lemon you have is hard to say.