The OW lounge at TXL is a BA Terraces lounge, so you shouldn't have any problems getting in there. YMMV with priority check-in, but if you present yourselves together, with your docs first, I suspect the efficient (and usually mum) check-in agents are unlikely to give you any grief.

As far as security goes, most gates at TXL have their own security screening checkpoints, so there is only one line available for use. More frequent TXL fliers can correct me on this if I'm wrong, since I've never flown out of terminal C, but it's been my experience that the lines aren't particularly long since most people go through security directly after checking in.