The main thing with lichens is air quality. No air pollutants are tolerated. If you are out in the country away from roads or BBQs then you may be able to keep them alive for a while. I think I have kept some alive for about a year.
I would think that dirt is not the stuff you want to use in planting your lichen. the image is of one growing over moss. I would attempt to use a moss bedding before using dirt.
On epiphytic lichens I have not heard of anyone who has suceeded using broken off branches but then who knows. Perhaps there is some info in the study in the link below.

Here is a link that might be useful: Marlene Liden study on epiphytic lichens in Sweden

Wow. Great link, I will have to read it later. I do live pretty much out in the country, so hopefully the air is not a problem. However, I would wonder if decomposing compost or dirt would actually simulate poor air quality, killing the lichen. The other times I have seen this kind of lichen it was growing on moss, so maybe that is a better idea, as it would probably make the air slightly better compared to compost no? Perhaps I will split the specimen in two and plant one with compost and one with moss as an experiment. About the epiphytes, the main reason I was asking was because one kind of native lichen I beleive called "lace lichen", which I have observed growing several feet in length, sometimes easily tears from the rest of itself and falls to the ground, so I was wondering if torn pieces would still grow not anchored to a branch. My initial guess would be yes, because that adaptation would come in handy if a piece fell onto another suitable branch and was able to continue reproducing.