Are you on one ticket or are these separate? If they are separate, then you may have a bit of a cascading domino effect.

In any case, TXL is a very small airport, and 85 minutes is easily enough time to make that connection. I don't know whether the DME flight will come into the main A gates or the 'portacabin' C section, but even if it's the latter, you'll need no more than 30 minutes. You will have to do passport control because the gates at TXL are all segregated from one another. Don't worry, I go through there a lot and you'll be just fine.

How long do you have at LHR?