Hi Ozzie
I don't know if this will put your mind at rest, but when I first stayed at the Lanzarote Princess in Playa Blanca (2000) there was a new hotel being built immediately in front of (or behind depending how you look at it! It was between the LP and the beach anyway) our hotel.
Although there was construction work being carried out for most of the day I can honestly say it didn't bother me, perhaps the wind was carrying most of the noise away from us, I don't know but it didn't spoil my holiday.
Work was just about finished when I stayed there a second time about ten months later but was still being carried out. Again, it didn't bother me.
Pippy