Falcao, who joined from Atletico Madrid in May, netted his fourth goal in five games from 12 yards, beating Fabien Audard after being felled by the Lorient goalkeeper.
The Brittany club did have chances to get back into the game, Sadio Diallo seeing an effort ruled out for offside midway through the first half.
However, the hosts always looked to be in control and will look to maintain their momentum when they face champions Paris Saint-Germain in a mouth-watering clash at the Parc des Princes next Sunday.
Lyon's winless run stretched to three matches as they were held to a goalless draw by Rennes at the Stade de Gerland.
Remi Garde's men headed into the game on the back of disappointing defeats to Reims and Evian, but were boosted by the return of striker Bafetimbi Gomis, who reportedly came close to joining Newcastle United in the transfer window.
Gomis, who netted 21 goals in all competitions last campaign, could not inspire the hosts to victory, however, as Rennes held on to make it just one defeat in five games for Philippe Montanier's men.
Nice won their second game in as many seasons at Lille's Stade Pierre-Mauroy, Claude Puel's men easing to a 2-0 victory.
Puel's side won by the same scoreline last season and had little difficulty in seeing off the 2010-11 champions once again, Argentinian striker Dario Cvitanich scoring a double.
Cvitanich - signed from Ajax in July 2012 - scored 22 goals for Nice last term, and it was his clinical finishing that proved to be the difference this time around.
The 29-year-old gave the visitors the lead after 20 minutes, latching on to a neat flick from Christian Bruls to hammer a shot past Victor Enyeama, before combining with the same player just before the break for his second.
