“Lande” is one of these relic case endings on nouns?
Yup, its pretty outdated.
So it’s more common to leave out the “e” and just say “auf dem Land”?
The whole thing Auf dem Land is a bit uncommon - outside this particular sentence - these days, I cannot imagine someone of my age (twenties) to use it. I feel as if you would normally specify where exactly (Im Dorf, In der Kleinstadt, In der ländlichen Region, Auf dem Bauernhof), the generic Auf dem Land isn’t used as much in comparison.
But if you want to use it, use it without the e