Les Merlus started the day second from bottom in the table, three points behind Metz and possessing a significantly worse goal difference of -28 compared to Les Grenats' -21.
Lorient's goals scored column was already superior, but head-to-head results take precedence in the French top flight, and both Les Merlus and Metz had one win over the other this term.
The duo had amassed three goals apiece, forcing the sixth classification rule to come into play - head-to-head goals scored away from home - and Metz had the superior total there with three compared to Lorient's two.
As a result, Lorient needed to beat already-relegated Clermont, hope that Metz lost to PSG and also enjoy an eight-goal swing in their favour to rise into the relegation/promotion playoff place.
Lyon pip Lens to Europa League place
Regis Le Bris's men did their bit with a 5-0 thrashing of Clermont at the Stade du Moustoir, while Metz suffered a 2-0 defeat to champions Paris Saint-Germain at home.
Such scorelines left the two relegation rivals on 29 points and a -23 goal difference, but despite Lorient's higher goals total, the head-to-head away goals tie-breaker sent them down in cruel fashion.
Metz are not assured of their Ligue 1 status, though, as they will face the winner of the Ligue 2 playoff final for the right to compete in the big time for 2024-25.
Elsewhere on the final day, Brest's 3-0 over Toulouse coupled with Lille's 2-2 draw with Nice dramatically sent Les Pirates straight into the Champions League league phase via a third-placed finish, forcing Les Dogues to go through qualifying.
Lyon - who were flirting with relegation at the start of the season - left it late to beat Strasbourg 2-1 thanks to an injury-time Alexandre Lacazette penalty, seeing them pip Lens to sixth spot.
The position would normally suffice for Europa Conference League qualification, but as Lyon are in the Coupe de France final with PSG, Pierre Sage's men have made it into the Europa League.
Les Gones will earn a ticket to the second-tier competition if they triumph in the cup final, whereas a PSG win would see the sixth-placed Ligue 1 team take the Europa League place.