What is the equivalent for Shimano Roller Brake grease?
Just as a confirmation on the comments above, I found a post on a separate forum definitely recommending to use the specific manufacturer grease, with a couple of the following points (Cited here for possible link decay):
For the grease itself-

Since my original post I have found some good information about lubricating the Shimano roller brakes.

Definitely use the roller brake grease available from Shimano (although it is fairly expensive), this is a demanding application due to the heat and forces generated within the brake and the lubricant is very high quality - it is a molybdenum disulphide based grease, and to me looked denser than what one usually finds say in automotive moly greases. Also it is lower viscosity so the brake will not drag and the grease can get into the braking surfaces more readily.


For application (And which indicates the poster spoke to someone at Shimano):


Very important to follow the instructions that come with the grease - main point is to insert the grease tube nozzle at least 12mm into the hole otherwise the grease will not reach the actual braking surface. If you look carefully you can see the cooling disc move a little when the nozzle is in far enough as it will push against it; come back just slightly from this position so the grease flows easily.

Shimano said you cannot really over do the grease as the excess will simply squeeze out and collect under the side cover. I was fortunate enough to be able to get an old brake and dismantle it - it looked to me like a rounded teaspoon or so of grease (say 10+mL) would be fine and my brake went well with this. Remember to rotate the wheel a bit while putting in the grease so it distributes evenly around inside the brake. Note that Shimano forbid dismantling of these brakes, and having done so with the old one I would say there is very little reason to anyway, and parts cannot be bought individually for repairs - still it was very interesting to see how it actually worked. The rollers (6) are not actually the brake, but push out three metal crescents that bind against the braking &quot;drum&quot; that is bonded to the centre of the cooling disc.



There are a couple of other points in the link, mostly just some tips about making application a bit easier. I could find absolutely nothing on a recommended substitute, which leads me to believe that the comments are correct, it's not worth it to try and find a substitute.