Catalyzes the formation of rosmarinic acid using caffeoyl-CoA and 3.4-dihydroxyphenyllactate as substrates. Can also use 4-coumaroyl-CoA and 4-hydroxyphenyllactate as substrates. Rosmarinic acid is an ester of caffeic acid and 3,4-dihydroxyphenyllactic acid. (2R)-3-(3,4-dihydroxyphenyl)lactate + (E)-caffeoyl-CoA = (R)-rosmarinate + CoA Optimum pH is 7.1. Optimum temperature is 45 degrees Celsius. Belongs to the plant acyltransferase family.