Not sure about NY but here is the ICC code path that I believe will require the emergency illumination.
Since your fire escape is existing and I assume you are replacing it because you do not meet the current egress requirements. I believe 504.1.2 clearly identifies the fire escape as part of the means of egress and emergency illumination is required..
2018 IEBC
504.1.1 New buildings.
Fire escapes shall not constitute any part of the required means of egress in new buildings.
504.1.2 Existing fire escapes.
Existing fire escapes shall continue to be accepted as a component in the means of egress in existing buildings only.
2018 IFC SECTION 1103
FIRE SAFETY REQUIREMENTS
FOR EXISTING BUILDINGS
1103.1 Required construction.
Existing buildings shall comply with not less than the minimum provisions specified in Table 1103.1 and as further enumerated in Sections 1103.2 through 1103.10.
Table 1103.1 sends you to 1104 which is required in all occupancies
1104.5 further identifies when emergency illumination is required by different thresholds such as occupancy, occupant load.
1104.5 Illumination emergency power.
Where means of egress illumination is provided, the power supply for means of egress illumination shall normally be provided by the premises’ electrical supply. In the event of power supply failure, illumination shall be automatically provided from an emergency system for the following occupancies where such occupancies require two or more means of egress:
1. Group A having 50 or more occupants.
Exception: Assembly occupancies used exclusively as a place of worship and having an occupant load of less than 300.
2. Group B buildings three or more stories in height, buildings with 100 or more occupants above or below a level of exit discharge serving the occupants or buildings with 1,000 or more total occupants.
3. Group E in interior exit access and exit stairways and ramps, corridors, windowless areas with student occupancy, shops and laboratories.
4. Group F having more than 100 occupants.
Exception: Buildings used only during daylight hours and that are provided with windows for natural light in accordance with the International Building Code.
5. Group I.
6. Group M.
Exception: Buildings less than 3,000 square feet (279 m2) in gross sales area on one story only, excluding mezzanines.
7. Group R-1.
Exception: Where each sleeping unit has direct access to the outside of the building at grade.
8. Group R-2.
Exception: Where each dwelling unit or sleeping unit has direct access to the outside of the building at grade.
1104.5.1 Emergency power duration and installation.
Emergency power for means of egress illumination shall be provided in accordance with Section 1203. In other than Group I-2, emergency power shall be provided for not less than 60 minutes for systems requiring emergency power.
