In a statement Lennon called on the two candidates on the ballot to “do better” and said “punching down on trans people and other minorities is not acceptable”.
Both Marra and South Scotland MSP Fagan have expressed scepticism about recent attempts by the Scottish Parliament to make it easier for an individual to change their legally recognised sex.
Lennon, who supported the reforms, also hit out against anonymous briefings during the contest.
She told Scotland News: “If you’re going to put yourself forward to be a man who is safeguarding women’s rights then think about how you treat the LGBTQ community as well in its entirety.
“I won’t be silenced. I’m not going anywhere. Frankly too many people have been pushed out of the Labour Party already in Scotland. That’s why we only have 11,000 members.”
Lennon wished both candidates well, called for “a battle of ideas” and warned the party against moving to the right.
Sarwar, who had led the party since 2021, declined to endorse a candidate during an Edinburgh Fringe event earlier this month.
But he warned the contenders and their teams against infighting.
Since his exit Dame Jackie Baillie has been acting leader of Scottish Labour.
As of last year, new rules prevent politicians from sitting at both Westminster and Holyrood at the same time.
There will not be a by-election for Sarwar’s Holyrood seat as he was elected via the regional list.
Monica Lennon, who had been in the Scottish Parliament for a decade but was not re-elected in May, is the next name on the Glasgow list.
The winner of the leadership contest will be announced on 19 September.