Pocket.
Lint is just added padding! 
Seriously, it's really not a problem. I have multiple ways of blowing, wiping or brushing any lint of a lens cap, if really needed. Heck, I can use my shirt tail, if necessary.
I "just say no" to UV/protection filters. Generally a waste of money. Especially the cheap, ones that can make a mess of your images.
Yeah, I have some UV/protection filters for my lenses (high quality, multi-coated), stored in my camera bag until they are really needed (shooting in a sand storm or at the seashore).
You're either cleaning the lens or cleaning the filter. Makes no difference, except that any dust specks on the filter are a little further from the lens so will be more "in focus" at smaller apertures on wide lenses (esp. if focused close).
And how much "protection" against physical impact can you realistically expect a thin piece of of glass? It's ever bit as possible that a shattered filter might be driven into the front of a lens and actually do damage, rather than provide some sort of mythical protection.
Lens hoods do a much better job protecting my lens while it's in use... Lens caps (with or without lint) do the protection job when it's not in use.
Getting down off of soapbox now.
I have a microfiber lens cleaning cloth in my left, front pants pocket all the time. That works to wipe off dust or lint when needed. There's also a bulb blower in my camera bag pocket (along with more microfiber cloths, lens cleaning fluid, a soft brush and sensor cleaning stuff. There's also "computer monitor wipes" and "canned air" in one of my travel cases, if needed for cleaning.
