Very short answer.. good lacing is due to several different genes, not just one. There's no specific "lace" gene. The various genes are either recessive, sex linked, semi- dominant and so on.
The main difference between gold and silver laced is that silver laced have the Silver gene(which is sex linked btw). But it's not that simple, as there are also other genes that "clean up" the silver for a whiter bird with less or no brassiness or some brown/red showing up somewhere(especially on the wing bows of roosters it seems).
Josie, I suspect you're thinking of Sex linked genes.
As for breeding to solid colored birds, it completely depends on what the solid colored bird is. If it's a solid black based on the E (extended black) which is dominant so most of the babies will turn out black.. the adults may have some brown or white striping or lacing on the breast/neck/
If the solid bird is white.. that is also very dependent on which white it is.. there's two- Dominant White and Recessive white. And then again it also very much depends on exactly what the white birds have "underneath that white".
Quite complicated question, that one is.