Gentlemen:
I suggest that the OP start by reading the definitions within 700.2; 701.2; & 702.2 to clarify what may be the correct steps in addressing this subject.
Based on what the OP ststed, IMHO, the existing gen is not a 'Life Safety' power source, as again IMHO, the egress lighting is 'Life Safety' in a multi-family structure.
Also, keep in mind that different localities have different opinions and codes regarding life safety issues. The best place to start is your local AHJ, either Electrical, Building or Fire.
