Tywin Lannister died without any other heir than Tyrion Lannister and his young wife Sansa, and rather than continue the mad fighting in Westeros Tyrion severed all ties and declared Casterly Rock neutral until a single King sat unquestioned on the Iron Throne. The fighting still continues, but House Lannister now takes in war orphans who are raised by Lady Sansa--it is this custom that first draws Daenerys Targaryen to Casterly Rock.