I don't know about Lady Lawson Street, but I've taken XLBs around the others, and they fit fine.
Honestly, as someone who drives them frequently, there really isn't that much difference between and XLB and a Gemini. There's a bit more tail swing that you've got to keep an eye on, but beyond that they'll both pretty much fit through the same places.
People seem to have got it into their heads that they're these huge monsters which don't fit anywhere, but the reality is that they can go to 99% of the places any other bus can.
The only place I can think of off the top of my head that an XLB won't fit is the left turn at the mini roundabout in Pilton on the 8, and the Geminis only just fit round there.