"The week starts on Monday."
Translation:Săptămâna începe luni.
To describe a recurring event like The team plays matches on Mondays we would say Echipa joacă meciuri în fiecare luni.
But I think you may be correct and lunea could already have this meaning, but it's safer to say în fiecare luni.
Yet if we want to say next Monday we say lunea următoare so here lunea wouldn't have a recurring sense. If we want to use luni to say next Monday we need something more verbose like următoarea zi de luni.