Ms Lawrence, convenor of campaign group Out for Independence, was described as “loud, fierce, supportive and committed”.
The organisation, the official LGBTQ+ wing of the SNP announced her death on Twitter, saying members were “heartbroken” to hear the news.
Ms Lawrence, who also worked as a TV producer, was reportedly found at home by police on Friday after friends and family had been unable to contact her.
Out for Independence said in a statement: “Out For Independence is heartbroken to announce the passing of our convener, Leeze Lawrence. It has been a huge shock.
"Leeze was a force of nature — loud, fierce, supportive and committed. Her life has been the kind of whirlwind she was, and she brought her vast network of contacts and experiences to Out For Independence to help us make new connections, build better policies and build shared solidarity between groups.
“She was dedicated to learning, becoming a better ally, and a better activist. In the last few months of her life, she was learning from GRT communities and we were planning with them the best way we could support LGBTQ+ Travellers. We hope to be able to continue that work in her memory.”
It added: “We will miss the way she went from no-nonsense organising with an iron will to being incredibly compassionate and looking after people who were struggling with abuse and harassment. There's no one way to describe her, except to say it has been a privilege to know her, and we miss her.”
Supporters took to Twitter to add their condolences to Ms Lawrence's family and friends.
Twitter user @mimmymum said: “I’m so very sad. I spoke with Leeze often and she was a wonderful woman – full of passion and drive to make the world a better, more inclusive and accepting place.”
Scottish Labour activist Heather Herbert said: “I'm very sorry to hear this news. Leeze and I didn't always agree, but we were always able to put aside our differences and work closely when it mattered.”
Michelle Campbell, SNP councillor for Erskine & Inchinnan, said: “A really scunnering bit of news to digest …sending my love to all who are feeling loss.”