The result left Monaco, who have already sold World Cup Golden Boot winner James Rodriguez to Real Madrid in the close season, in 12th place with four points from as many games.
Rodriguez's fellow Colombia international Falcao was not listed on the team sheet on Saturday and he and his agent Jorge Mendes were seen chatting on the phone at halftime.
Falcao, who missed the World Cup after suffering a serious knee injury, has been linked with several top European clubs.
"Dream has come true #HalaMadrid (Come on Madrid)" Falcao tweeted after the game, before deleting it from his account.
"I cannot say more than the fact he was unavailable," coach Leonardo Jardim told a news conference.
Monaco were bought by Russian billionaire Dmitry Rybolovlev late in 2011 and have spent big money to match Qatar-owned Paris St Germain's ambitions, but they have now taken several steps back with Rodriguez's sale and Falcao's likely departure.
Last May, Rybolovlev was ordered by a Swiss court to pay Elena Rybolovleva about 3.3 billion euros (2.61 billion pounds) as a divorce settlement.
"I'm not the one who defines the project of the club," said Jardim when asked about Monaco's strategy.
On the pitch, Lille, who are second on eight points, went ahead after 18 minutes when Nolan Roux beat Danijel Subasic with a low shot after being set up by Ryan Mendes.
Monaco, who spent over 100 million euros to lure Falcao, Rodriguez and Portugal midfielder Joao Moutinho, were toothless until they equalised in the 61st minute.
Home grown Yannick Ferreira Carrasco outpaced the Lille defence before striker Dimitar Berbatov tapped home his cross.
Lille coach Rene Girard was sent off for arguing with the referee.
Champions Paris St Germain can move up to second spot if they beat visitors St Etienne on Sunday (2000 GMT).
(Reporting by Julien Pretot; Editing by Ken Ferris)
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