D'Alessio JM, Gerard GF.

Nucleic Acids Res. 1988 Mar 25;16(5):1999-2014.

Second-strand cDNA synthesis with E. coli DNA polymerase I and RNase H: the fate of information at the mRNA 5' terminus and the effect of E. coli DNA ligase.

RNAse H (also provided by the reverse-transcriptase) and ligase are not strictly necessary during second-strand synthesis.