From Lekkie's website;

For BBS02; Compatibility1-11 speed (most chains), Sram Eagle 12-speed.

Does not fit : Shimano 12-speed, KMC X101, KMC Z1eHX

For BBHD; Compatibility1-11 speed (most chains), Sram Eagle 12-speed.

Does not fit : Shimano 12-speed, KMC X101, KMC Z1eHX

For the PRO 40t model; BBHD

Compatibility 10-12 speed(most chains), Sram Eagle 12-speed, Shimano 12-speed

Does not fit KMC X101, KMC Z1eHX chains

So Yup the PRO 40t seems to be the one choice for a 12 speed Shimano

The Pro model seems to be about the most expensive chainring Lekkie produces!

And I don't see anything for BBS02 / PRO 40t, just BBHD.