It depends what you mean when you say "lime".
I think the limiting factor would be the pH of the substrate.
Hydrated lime (calcium hydroxide), the stuff used by builders, is extremely alkaline (ph 12.4), which is an irritant to most plant and animal tissue and would probably be quickly lethal to all but the most extremophile organisms. Calcium oxide (quicklime) has a pH of 12.8, and has been used as a weapon:
https://en.wikipedia.org/wiki/Calcium_oxide#Use_as_a_weapon.
Garden lime (limestone or calcium carbonate) has a pH of 9.4, and lichens will grow on this.
In terms of concrete and mortar (which contain hydrated lime or sometimes quicklime) this has been largely neutralised by the chemical reactions that take place as it sets. There are lichens that will grow on concrete, cement and limestone. Here are some growing in Ireland (where limestone is also a common rock), separated to species:
http://www.lichens.ie/view-lichens-by/lichens-by-habitat/limestone-burren-lichens/
I'm not sure how you'd go about putting together a mix that would encourage lichens (see
https://permies.com/t/55379/fungi/Loving-lichens for a discussion ) for such an alkaline substrate, but I would suggest one aiming for a pH around 9.4, which would be the most likely pH of the natural substrate of these lichens.