Mainz is boring with tons of poor restaurants catering to its many tourists and students.

My recommendation would be to use the luggage storage at FRA, arrivals B. Then walk to the nearby entrance to the local train station. Take any S-Bahn (cars in reddish color) from track 1 and get off at Frankfurt Hauptwache. For luxury shopping and/or upscale restaurants, walk West, visiting Goethestr., Neue Rothofstr. and (for eating out or drinks) Fressgass.

Alternatively, explore in the Southern direction from Hauptwache. The aforementioned Kleinmarkthalle is good for lunch and local specialties. Do not miss the "new old town" which has recently been restored. Have a coffee at the Huhnermarkt (former market for chickens). If interested in culture, visit the Cathedral, the Paulskirche, the Roemer (town hall), the Goethe-Haus (birthplace of Germany's most famous poet), or the nearby Romantik-Museum (museum on romanticism). For fine arts, go to the Staedel museum on the other side of the river.

If the weather is good and arts and culture isn't your thing, just head South from Hauptwache towards the Main and have a stroll along the river.

Spending 10 hours at one of LH's mediocre business lounges seem like a major punishment to me. If you don't want to leave the airport, I'd at least get a day room at the airport Hilton or such.