if it's mineral oil it should be ok, but I would use the Shimano oil just be to safe, I don't know a whole lot about oils (just how to bleed brakes), I don't know if the lhm oil has any additives that may damage the seals in a Shimano brake, worth checking that out before buying, also make sure it is the same viscosity (this is why you can't use Magura Blood in shimano brakes) otherwise you may find yourself without brake power at a critical moment!
It is best to use the shimano stuff. I have put lhm/ magura fluid in and it tends to make the lever feel sluggish. It seems thicker when you apply the brakes. Not saying that you shouldn't use lhm as the brakes still work but it will result in a horrible feel at the lever. Hope this helps
Any mineral oil will do. Shimano stuff is just re-badged stuff sold on at a massively inflated price. Kinda like all 'bike specific' oils and greases, that you can get for a fraction of the price, when it doesn't have a picture of a bike on the front!
