Long time since I have been there but both Los Zocos and the Teguisol in Costa Teguise on Lanzarote have 2 bed apartments. Also I think it was the Ocean Club apartments in Puerto del Carmen had two beds - this last one is a much smaller complex than the other two.
You or your sister would need to check recent review though.
Robbies tip is good, search on the main tour ops sites and then try and get it cheaper by booking flights and apartment direct unless she is a worrier in which case might be better with a package.