Is the area in consideration in full or partial sun, or full shade? Is the soil dry, moist or wet most of the time?

Unfortunately, whatever you plant beneath the canopy of the lime trees will become sticky and possibly develop sooty mould every summer - certain common varieties of lime (Tilia) have heavy aphid infestations every summer, and their honeydew is what covers everything with sticky stuff... I haven't forgotten the last time I mistakenly parked my (white) car under one and left it there for five days - when I got back, it was covered in glue like, black sticky stuff, with anything and everything from leaves and plant debris to plastic bags and bits of paper blown by the wind forming a collage on top. I couldn't even see through the windscreen.... Still, it did explain why I was able to park in that street, which I didn't expect to be able to, too close to the station - clearly, everyone else avoided that space....

With large trees like these, its next to impossible to spray with systemic insecticide fortnightly (which would solve the problem) or blast with a hose every couple of days to clear the aphids.

Try some of the larger varieties of hosta.