Although both words can be found in dictionaries, I'm constantly forgetting which one is which.
Are there any mnemonic rules that would help me remembering them?
Lose has lost one of its o's.
Loose has an extra o, like an extra hole in a loose knot.
(Honestly, though, remembering just the first one should be enough to get you through everyday life).
If I lose something, it has become lost not loost.
If the goose gets loose, you lose your job.
(2 o's in goose and loose. and they rhyme. once you know that, you're set.)
Looose (stretch the o) is nice and large, while lose is small and easy to misplace?
(nice and large, I guess like a pair of misfitting pants or something, I don't know)
You have a regular spelling in loose, adjective, and a special spelling in to lose, verb. I would say the drop of one o is an optical help to distinguish the two words.
As a mnemonic help you can arrange alphabetically:
A adjective loose with Ŕegular spelling
V verb lose with Śpecial spelling.
Try if this helps. If not, you have to invent something better. I did such things sometimes with my pupils to improve their creativeness to invent memory aids on their own.