Soup dragon may be your man for this but
this site gives
Rutilus Leo for Red Lion and ex, de, a, ab, abs, quo for "from", (quo is probably best for a place). It can't work out a translation for "of"
Of course "Bath" works for something you bathe in but not for the city so go with "Aquae Sulis". "A" lion is probably a different word (ending) to "The" Lion.
Sadly English and Latin don't work the same way so for example there isn't a word that just means "red" it sort of depends on how red, how many red things, what's red and when it's red, so words like Rubeus, rufus, rubicundu(lu)s and ruber all mean red in different ways. Rutilus means red but tending to golden yellow or even ginger haired according to my old latin dictionary:
I'm tempted to say "Leo Rufus" or "Leo quo Aqvae Svlis"