Your broadband speed is the speed that your router can get over the phone line to your ISP. This has nothing to do with the speed over your (power line or other) local area network. The Lidl devices claim a throughput of 85Mbps but I would imagine that in practice the actual throughput would be a lot lower but still higher than many broadband connections (e.g. > c. 3Mbps or whatever) which means that your LAN should not be the bottleneck. This Wikipedia article on the technology might be of interest. [broken link removed] includes some background information which might be of interest here too.
Have these setup in my own house and someone elses for the past year and a half. Ones a (relatively) new build and the other quite old - and works flawlessly in each. Problems may occur if house has been badly wired - thats the variable.
Just in case you need it, theres 200MB/sec rated adapters also (which is what i'm using ..netgear kit).