Catalysis of the reactions: (1) GTP + F420-0 + L-glutamate = GDP + phosphate + F420-1, and (2) GTP + F420-1 + L-glutamate = GDP + phosphate + gamma-F420-2. This is the GTP-dependent successive addition of two L-glutamates to the L-lactyl phosphodiester of 7,8-didemethyl-8-hydroxy-5-deazariboflavin (F420-0) to form F420-0-glutamyl-glutamate (F420-2), with a gamma-linkage between the two glutamates.