Muhkat Lomorki
Draconic Sorcerer
Actually, ranger might work better considering the character is an explorer, which makes things a hundred times easier.A 5e Lizardfolk dinosaur-rider is easy. The Beastmaster Ranger can have a CR 1/4 creature as a pet. Hadrosauruses are CR 1/4, Dinosaurs, and Large (meaning you can mount them). Bam, done.
If you specifically want to be a Fighter who rides a dinosaur, ask your GM to let you buy one. A Warhorse is CR 1/2 and 400 gp, there's no reason you couldn't buy a less powerful Hadrosaur unless the setting doesn't allow for dinosaur trade.
As for the background I established for where he comes from, how would a DM work that into the plot? I'd imagine it would be pretty easy, since looking for powerful McGuffins is basically what most adventurers are doing anyway; this is just justifies it even more.