The Brazil international suffered his latest fitness setback on 9 February after the defensive midfielder was forced off inside 16 minutes of the Merseyside derby.
The 27-year-old was reported to be set for a month on the sidelines, but it appears Lucas could be ahead of schedule after he uploaded a video of a light training session in Brazil.
Lucas posted the clip of a short jog on Friday night, giving Liverpool fans a much-needed boost after their Europa League exit on Thursday night.