Lumumba was due to return to training with the remainder of the Demons' five-year-plus players on Monday, but he opted to take part in a light session with Melbourne's younger players at Gosch's Paddock on Friday.
The former Magpie joined Melbourne during the NAB AFL Trade Period in a three-way deal that also sent ex-Demon Mitch Clark to Geelong and former Cat Travis Varcoe to Collingwood.
Lumumba, who played 199 games in a 10-year career at Collingwood, looms as a key player for Melbourne in 2015, adding some run and quality ball use out of defence.
He played in Collingwood's 2010 premiership team and was also named All Australian in the same season.
Lumumba, who turns 28 on Saturday, left the Magpies in what president Eddie McGuire described as an "amicable" parting, following two tumultuous seasons at the club.
The attacking defender's form never suffered, however, as he finished fourth in Collingwood's Copeland Trophy count in 2014 and fifth in 2013.
Heritier Lumumba during his first training session as a Melbourne player. Pictures: melbournefc.com.au
