What is the approximate optimal temperature that the enzyme lactose works best at to allow expression of beta-galactosidase in bacterial strains?

check supplier info.

seen a lot of expmts run at 37C, but there's thermal resist enzyme that can be used at 65C, and others have run at room temp.

if in doubt you could always do a quick study with temp as a variable... otherwise I'd talk to the manufacturer if you don't have the data on hand.