CPF member pbs357 has documented success powering a "new" Wolf-Eyes D26 9V lamp assembly with two (2) LightHound-sourced RCR123a protected 3.7V batteries. I personally run a DigiLight DRB-9VHP 9V lamp assembly (175 lumens claimed by the manufacturer) with two (2) LightHound RCR123a protected batteries.
Other CPF members have reported that their DRB-9VHP 9V lamps require two or more clicks to light when driven by a pair of protected RCR123a's. Hence my disclaimer of YMMV "Your Mileage May Vary". Finding a high output 9V lamp assembly that reliably runs on a pair of protected RCR123a Li-ion rechargeable batteries appears to be something of a crap-shoot.
For example, I own a G&P G90 9V lamp that will light up instantly when powered by two 17XXX-series protected batteries or two LIR123a unprotected batteries but requires two clicks to light with a pair of protected RCR123a's. My DigiLight DRB-9VHP lights instantly when driven by two (2) LightHound RCR123a protected batteries. It's possible that my DigiLight DRB-9VHP lamp either draws less current at start-up than most or my LightHound protected RCR123a batteries protection circuits can supply more current than other similar batteries. In any case, my personal experience with the DigiLight 9V lamp does not appear to be typical.
The Wolf-Eyes D26 appears to be one of the better bets for your application according to
The Rechargeable Battery Compatibility Chart.