Is Tyrion infertile ?

[Castellan]

I just don't think the women would want to have his baby. I don't think getting pregnant to a lord is necessarily a paycheck. Its only highborn bastards that may generally get some kind of recognition and obligation. Gendry getting an apprenticeship seems a bit unusual. Children of prostitutes especially may be just completely ignored. And the women would likely not want to risk having a child who might be a dwarf. Its quite an aweful thing to be in Westeros, to be physically disabled and seen as an evil imp. I think those women have enough to contend with without contemplating trying to raise a child with dwarfism in a brothel, not to mention they probably subscribe to the same prejudices themselves.

 

Another interpretation of Lanna is she is the child of Gerion Lannister.