The LUXX lounge is poor even by contract lounge standards. And it's landside. I wouldn't bother despite the fact that the security check upon re-entering the secure area in A is likely to be quick and painless due to low traffic.

Are you flying LH? If you got an Amex Plat, you may use it to access a LH lounge. Currently, LH also accepts LH eco passengers into its lounges for a fee of EUR 39. I don't think the lounges are worth EUR 39 but just mentioning it for the sake of completeness.

Without any option of complimentary access to a lounge other than the LUXX, it's a tough choice. In normal times, I'd suggest the restaurant Deli Bros (decent quality for the price) but it's still closed. So I guess in that situation, I might purchase a sandwich and a drink at Heberer (near the root of A) and find myself a currently unused gate where it's quiet with tons of free seats.

And if I found enough time on my hands to go landside, I'd rather opt for the "Airport shopping mall" (in A and B, lower level). They've got a decent Thai fast-food restaurant and a bunch of other fast food options (McD, KFC etc.). Not haute cuisine and bubbly exactly but cheap and I'd still prefer that over the LUXX lounge.)

EDIT: If your layover is quite long, another option is Paulaner's. Go landside, walk towards the Squaire (long-distance terminal), take an escalator up in the direction of the big blue KPMG sign. Paulaner's is simple Bavarian restaurant which is good value. Their lunch special currently costs just EUR 8.90 and a pint of a Munich lager (Paulaner Münchner Hell) is EUR 4.60.