A lens mold carrier (1; 2) comprises:a frame (10; 20) extending in a plane (x,y; u,v) and comprising a plurality of individual compartments (100; 200);at least one mold unit (11; 21) arranged in one of the individual compartments (100; 200) in a manner secured against falling out, the at least one mold unit (11; 21) including an adapter piece (110; 210) and a lens mold (112; 212) fixedly connected to the adapter piece (110; 210).The adapter piece (110; 210) is floatingly arranged within the compartment (100; 200) to allow for limited movement of the adapter piece (110; 210) within the compartment (100; 200) at least in a translation plane parallel to or coincident with the plane (x,y; u,v) in which the frame (10; 20) extends.