You can use the
Raster Calculator tool:
It is quite a generic and powerful tool, in your case the logic should be however pretty straightforward.
cover layer (channel 1, hence
cover@1) has a value of 1 where you want to retain data from the
LAI layer (channel 1, hence
LAI@1) , and 0 where you want to discard them, the Expression could be very simple:
"cover@1" * "LAI@1"
If you want to create a mask (i.e. have null/empty pixels where
cover is zero) a kind of hack can come in handy:
cover= 1 -> the output will be equal to LAI
cover= 0 -> the output would be LAI/0, which is impossible, thus the Raster Calculator returns a null value.
To avoid errors and artifacts, make sure both layers have the same reference system and resolution ;)