An additive for a resist underlayer film-forming composition, including a copolymer having structural units of the following Formulae (1) to (3): wherein R1s are each independently a hydrogen atom or a methyl group, R2 is a C1-3 alkylene group, A is a protecting group, R3 is an organic group having 4 to 7-membered ring lactone skeleton, adamantane skeleton, tricyclodecane skeleton, or norbornane skeleton, and R4 is a linear, branched, or cyclic organic group having a carbon atom number of 1 to 12, wherein at least one hydrogen atom is substituted with a fluoro group and that optionally has at least one hydroxy group as a substituent. A resist underlayer film-forming composition for lithography including additive, a resin that is different from copolymer, organic acid, crosslinker, and solvent, wherein the copolymer's content is 3 parts by mass to 40 parts by mass relative to 100 parts by mass of the resin.