Falcao, who joined from Atletico Madrid this season for a 60-million-euro transfer fee, netted his fourth league goal from the penalty spot after being brought down in the sixth minute.
Monaco have 13 points from five games and lead second-placed St Etienne by one point and third-placed Paris St Germain by two after the defending champions beat Girondins Bordeaux 2-0 away on Friday.
The Russian-backed team from the principality could have doubled the tally shortly before the break but Fabinho's strike from the edge of the box smashed Fabien Audard's left post.
Lorient, who are 13th on six points, were barely a threat against promoted Monaco.
Colombia striker Falcao, back from international duty, was replaced in the 62nd minute by Emmanuel Riviere, who failed to add to his five Ligue 1 goals in a dull encounter.