Lichen can indeed grow on the ground, as long as the ground is cool and damp, or at least shaded from hot midday sun.
Im not sure it could grow that thick in a month, as they are very slow growing, which is why the oldest gravestones tend to be the ones with lichens.

There are some lichens such as the dog lichen (Peltigera canina) that grow happily in lawns and are relatively quick to spread. I find the patches in my lawn quite attractive and they are limited to the areas I don't maintain closely. Have a look at the link for more info

Here is a link that might be useful: rhs lawn lichens

Thank you for the information. I'll still post a photo this weekend. The ?lichen? is as flat as paper, but has grown horizontally. (at first, it though it was new leaves of the clover I weeded the week prior.

As it has appeared in several tiny patches, I'm worried that it will take over my moss. Any chance?