Lea Michele Check Out My Hot Ex-Gigolo ... Coach

7/3/2014 2:25 PM PDT

Lea Michele stepped out publicly for the first time with her new guy Matthew Paetz ... but the photos look about as genuine as Matthew's claim that he wasn't a gigolo.

The pics show Lea and Matthew, guns out, on a leisurely hike -- and look like classic set up shots pre-planned with photo agencies. They're even wearing matching sneakers.

Our take -- Lea is screaming to the world she doesn't care about Paetz's past -- remember he claims he was only coaching gigolos, not doing the gigoloing himself.

Or maybe she's just showing off her new project -- a bad boy to fix.