I'm not very good at this, but I found in my copy of Nimmergut's Orden & Ehrenzeichen a medal that looks exactly like this one, except for a few small differences. The one in the book is from Hessen-Homburg, the writing and everything looks the same except it has a crowned F instead of an L, and the date under the F looks like it reads 4 IUNI 1850.
The Landgraf of Hessen-Homburg from 1829-1839 was Ludwig, so perhaps they hadn't changed the cypher by 1840 and that's why your medal has a L on it??? The Landgrave from 1848-1866 was Ferdinand which would account for the crowned F in the book.