Moby hit headlines after he told The Guardian that hearing the 1970 track on Spotify left him "taken aback" by what he viewed as "gross and transphobic" lyrics.
Dave Davies opened up about the row, saying he was worried the comments could cause a major backlash against the legendary British band.
"I am highly insulted that Moby would accuse my brother of being 'unevolved' or transphobic in any way," he wrote on X/Twitter.
He told The Telegraph newspaper: "I found it quite upsetting that he said it (Lola) was transphobic and old-fashioned.
"I worried that it could turn people against us because it can feel like people are becoming weirder by the day. They are always quick to judge and make assumptions about others. It is very rigid thinking. They don't know that there is always a backstory. It can be dangerous to smear people."
He went on to say that his brother Ray asked him "who the f*** is Moby?" when they spoke on the phone.
"He wasn't happy at all," Dave said.
He added Moby's comments about Lola stung as The Kinks were friendly with members of the transgender community.
"(Lola) was fun and quite beautiful. It was about real people and real people's antics. There is nothing nasty about it."
Lola's lyrics were inspired by Ray Davies' conversations with drag queens and describe an encounter between a man and a transgender woman at a bar in London.
Dave added: "We had a lot of people like that backstage, which is what happens when you are called the Kinks. What we learned growing up in that band is that everyone is different: No one is one thing ..."
Lifeline 13 11 14
Fullstop Australia 1800 385 578
12°C