Yes you can plant most citrus seeds from store fruit if you take a few precautions.
After removing your seeds from the Lemon ,immediately soak them in warmwater to remove all the residual sugar and flesh off the seeds. This is to prevent fungus and mold from living off the sugars and hurting the seedling before it has germinated. Take sterile compost or soil and plant your seedlings one half inch below the soil surface. Voice in the soil and then cover the pot or trade to prevent the soil and seed from drying out. It may take up to one to two months for the seed to germinate. As soon as the seed germinates it needs light immediately. This might not necessarily mean direct sunlight if you're sprouting these in the winter time but it's going to need a bright light source.
Currently there are no genetically modified lemon trees but that might not be the case forever. Please keep this in mind.
A interesting thing about citrus seeds is that you may get several seedlings from each seed. One of these will be from the embryo formed due to pollination in the orchard, but the others will be "apomictic" seedlings which are vegetatively produced. That means that the apomictic seedlings will be exact genetic reproductions of the tree on which the fruit was formed, they are clonal seedlings. The one seedling produced by pollination will not be clonal as it will carry genetic material from the pollen parent (father) as well as the seed parent (mother). In any case, you should have a lemon tree, and it will very likely produce tasty lemons in about 15 years! I thought you would want to know that it will take a long time unless you graft from the seedling to a mature lemon tree. A mature tree may often be purchased at a nursery in the house plant section. There are dwarf house plant lemons from which you may also choose. Grafting may reduce the time for fruit production to only 5 years or so. And the trees can be bonsaied to produce shorter varieties although production will be reduced