Many think this is the case. In fact it was Aldi who was set up by two brothers, who later fell out and set up separate companies that continue to share the same logos and suppliers. Read about them
here.
Lidl was set up by members of the Swartz family. Markt is the German for 'market' and 'swartz' in German means 'black'. so, not wanting to call their company 'Swartz Markt', or 'Black Market', they paid for the use of the surname of a friend, who was a retired teacher named Lidl.
Read about it
here.