Totally different companies now. They do have an agreement to not compete in most countries though. The only countries both are present are Germany and the United States.
In my experience in the US, grocery stores have way more competition than stores in most other retail sectors. It's also one of the few retail sectors in the US where regional brands tend to outcompete the national brands. I'm not sure the main cause of that, but I'd be interested to find out.
I wonder who would bring the suit if they're divvying up the world country by country. Who has jurisdiction? The EU?
Giving this marginally more thought, maybe the agreement is simply on use of the shared brand name, and that's what the agreement covers? I note both are active in the US, but under different names. That might just be enough to keep regulators happy.
https://en.wikipedia.org/wiki/Lidl
Besides, why should the Government force a company to open stores where they have chosen not to?