I can't help with a flashlight-specific bag. However, I'll point out that the Fenix LD10 comes with a strong clip that allows the torch to be attached to all kinds of different things. For example, my LD10 is attached to a pocket in my man bag. Even if I didn't have the clip, my man bag has a small pocket that's perfect for the LD10. Frankly, with all the things that I think are necessary to carry, I could not manage too well without a small man bag, or I'd have to make compromises that I'd rather not make.

Maybe contact Fenix and see if the clip will fit your L1D.