In response, the LNP president, Mr Spence, said: "People who aren't team players often find it difficult being a member of a political party."
In a letter to members, Mr Lindsay said he and Richmond mayor John Wharton quit the LNP this week.
"You may recall that we were unfairly hit with suspension in December for making a constructive comment about the loss of the state election," he wrote.
"Since then, the president and state executive have continued to refuse to acknowledge our point that the LNP needs to be politically smarter if the party is ever to beat the ALP.
"Following the loss of the last state election, there is now very little prospect of having an LNP member elected here in Townsville in the next eight years (apart from Senator Ian Macdonald if he is preselected again)."
In a letter to the LNP state executive, Mr Lindsay said the party's campaign had "failed dismally" and Labor was probably guaranteed another two terms in Queensland.
"Following the state election loss, I was moved to make my first public statement in the seven years since my retirement," he wrote.
"The guts of it was that the party continues to lose elections due to poor political decisions and has been unable to come anywhere near matching the Labor machine when it comes to being politically smart."
Mr Lindsay said he was astonished to be suspended, and the action was politically unwise, with news of his suspension triggering two weeks of "bad media" and stunning the business community and donors.
His resignation comes after the LNP state executive decided to extend the suspension for another six months.
"Since the latest decision, I have taken the time to count to ten. I have decided that I do not want to spend the next six months being desperately unhappy with what the party has done to me," he wrote.
It is understood Mr Lindsay has joined the ACT branch of the Liberal party.
Mr Lindsay said he had devoted more than 40 years of continuous service and held the honour of winning more elections than any other LNP member - 10 in a row.
He represented the Queensland federal division of Herbert from 1996 to 2010.
Mr Lindsay had his membership suspended in late 2017 after he criticised the party over the Queensland election campaign.