I don't know how long the shelf life is. I use the 14500 (AA sized) rechargeable lithiums in my single-AA sized flashlights (the ones that can take the higher voltage, that is). I use the light on my belt several times daily, probably averaging 5-10 minutes per day (usually in the middle brightness setting). A rechargeable lithium will last me several months. The other lithium-equipped single-AA sized flashlight I have sit unused for up to six months at a time and they're always fine when I do get around to using them or swap them out to use as my daily carry light. They last several months in use after sitting for those six months. Unscientific, but it doesn't seem to me that they lose much charge.

My wife's Fenix E01 did indeed have alkalines in it. You cannot use the higher voltage rechargeable lithiums in that light. Rechargeable NiMH are fine however. I don't use primary lithiums except for extremely long "not used" scenarios where I want them to work when I finally do need them. In my case, that means in firearm mounted weapons lights. Everywhere else I try to use rechargeables (except, unfortunately, in my wife's Fenix that got ruined by the alkaline battery - I forgot about that one).