Yes the battery is the same on all their light's. Just the bulb and reflectors are different on the lights.
Lemax uses 2 different wattage ballasts as we also do, but we use military grade ballasts (35/50 or 50/70).
Actually we use 2 different bulbs and different Igniters for the 2 different lights, while Lemax uses the same OSRAM or Philips D1S 35 watt rated bulb/igniter assby (1 piece) for all 3 lights, even 70 watts.
We use a 35 watt GE D2S bulb made in Hungary (best in class) for the 35/50 and a XeSparQ igniter / socket (patented) for fast bulb replacement 1 to 2 minutes (no tools)
vs 20 minutes and special tools needed for the Lemax bulbs.
We use a special high power and very expensive (3X $) Philips bulb for the 50/70 or a Superpower, Philips DL50/740 (not a "fatboy")
For our proposed "Ultra" (80 but more likely 85 watt) Superpower or standard (LX70) head our XV-85 ULTRA (60/85 most likely) we use the same XeSparQ Igniter/socket and the Philips DL50 "Fatboy" to handle 85 watts.