Last week an opposition ticket headed by current directors Paul Williams and Mick Power, along with Lions triple-premiership coach Leigh Matthews, sought to overthrow Johnson.
Johnson stood firm after being asked to resign, saying he would have his fate decided at December's Annual General Meeting.
However, the Williams-Power-Matthews ticket do not wish to wait that long, and are now pushing for an EGM.
The Lion's Roar - an advocacy group established earlier this year - have sent request forms to voting members to exercise their rights to an EGM.
After putting an expression of interest form on its website eight days ago, The Lion's Roar received feedback from 1400 members.
Williams-Power-Matthews need five per cent of the 11,000 full voting Lions members – 550 in total - to sign and submit the requisition form for the EGM to go ahead.
The letter to members carries an address from the Williams-Power-Matthews ticket.
The Lion's Roar says it offered Johnson the same opportunity, but the club denies receiving the invitation.
"We at The Lion's Roar are not advocating support for either ticket in this dispute but, in the absence of an amicable resolution, we believe calling for an EGM is now the most practical solution for ending the division," its letter says.
The rival ticket was unsatisfied with Johnson's handling of the pursuit of Paul Roos in the wake of Michael Voss' sacking.
Johnson said his dealings with Roos had gone well and pointed to his other achievements as chairman that included the recent unveiling of a $60 million elite training facility to open in 2016.
If Williams-Power-Matthews get the necessary numbers to lodge a request, the club has 21 days to set a date for an EGM at some stage in the following two months.
Twitter: @AFL_mikewhiting
