"I have no legal rights over Carmen. The woman who gives birth has all legal rights," he told CNN from the Bangkok apartment he shares with husband Manuel Santos, their two-year-old son and baby Carmen.
The drama began a week after Carmen was born in January. The day before Lake planned to take Carmen to get a U.S. passport, he received a text from the translator for Patidta Kusolsang, the surrogate mother. She said she wanted to keep the baby.
Now Carmen's future is in the hands of the Thai courts.
The legal battle comes during a particularly complicated time. Thailand once had a booming surrogacy industry catering to foreign couples, but a series of scandals led the country's military rulers to ban the practice.
The new law takes effect at the end of the month and makes surrogacy for profit a criminal offense.
Carmen's fathers are hoping to take advantage of a temporary provision that would allow them to leave with Carmen, but it defines intended parents as a "husband and wife."
According to Lake, the baby is biologically his with an egg donor. He believes Kusolsang, the surrogate, changed her mind about giving them the baby after she found out they were gay.
In their first meeting to try and resolve the dispute, "she declared that we were not an ordinary family," he said.
Surrogate: I changed my mind
Kusolsang denied their sexual orientation is the issue, saying she cares only for the safety for her child.
"I miss her every day," Kusolsang said. "You see how cruel the world today. And I just don't know what they are going to do with my baby."
She told CNN she changed her mind months ago about giving up the baby and tried in vain to get more information about the intended parents.
Kusolsang has filed a claim with the Thai police and written a letter to the U.S. embassy. She said she will return the couple's money if she can have the baby.
"I don't want his money, not even one single baht," she said.
Lake and Santos plan to go to court on July 30 to file their petition. Stuck in Bangkok, they've been trying to raise money for their legal battle online. Their Fundly page
currently shows contributions of more than $25,000.
"In our mind there is not a possibility that we can lose Carmen," Lake said. "She is our daughter and our daughter belongs with us."
He pledges to stay in Thailand as long as the battle takes.