Apples do not grow true to seed. Having said that, apples grown from seed are likely to carry along some (and often many) characteristics of the parents. Certain varieties in particular are known for passing on more similar characteristics in their seedlings. An example of this is the Snow Apple (Fameuse). This is the parent of the McIntosh and grandparent of countless varieties. The seedlings that you have in hand will probably have numerous traits of the Lady, but to get a true Lady you would need to graft a bud or scion from the parent tree onto another apple tree or rootstock. Remember also that a tree grown from seed will want to grow into a "standard size apple" which, depending on the variety, can be in excess of 30 feet. Most backyard gardeners would prefer a tree that is a bit more manageable, hence the use of size controlling rootstocks. With use of different rootstocks, you can control the ultimate size of the tree anywhere from around 5 feet to full sized standards. Most homeowners opt for trees grafted on semi-dwarf stocks. These limit the trees to 8 - 15 feet tall. If you have your heart set on planting a Lady are numerous places to buy them but the seedlings are always a roll of the genetic dice.
Mike