I've lost masks but never during a dive, if that's what you mean.
I had one kicked off my head during a dive by another diver, and that experience makes me think that your lanyard might not be such a good idea. When the mask is fully off your head and you need to replace it, then I believe the lanyard will provide a complication in a situation where you really want to keep things simple. That said, I was lucky in that situation that I manged to catch the mask out of reflex and if I had missed it, a lanyard may have saved my dive.
In the OW course you train for diving with a lost mask. Sadly, we spend time on the CESA (which imho is a pointless exercise) instead of spending time on helping a buddy with a lost mask make an ascent and/or stops.... Most divers don't see this until much later in their learning. The first time I saw this as a performance requirement was in a trimix course.
As for the lanyard. I think the basic idea of not wanting your mask to slip off your head (somehow) is good. This can be addressed without a lanyard, however. By ensuring that you have the right equipment (mask band, cap etc.) and that you employ them correctly. The lanyard seems to me to be a solution to the wrong problem. If you drill down to the root cause of a mask "slipping off" then you're probably going to find that either the cap was too big (poor fit) or the mask strap was too high on the back of the head.
As for surface swims etc. either the mask is on or it's around your neck. In neither of those positions can it slip off without you noticing.
In the case of a mask strap breaking during a dive, most divers who I know that make dives that require you to solve all problems underwater (a) check the strap before the dive and (b) carry a backup.
All in all, I can imagine why some people would see an application for this. In my case, I strongly believe in keeping things as simple as possible and to solve problems with skills instead of adding more gear. For myself I can see no application.
R..
