I think the 'thick Paddies joke' was supposed to be ironic. ie: it's a joke where the punchline demonstrates that it's actually lambasting 'thick Irish jokes', and as such, in this context Lox is likewise lambasting Thatchers own golliwog joke..
Maybe you recognised that and still thought it inappropriate?
Such humour which highlights issues such as racism, where there has always been a nicely virulant cesspool of 'traditional' stereotype based jokes, is an interesting one though.
Particularly where it does and doesn't work, or can be seen as acceptable?