The 35-year-old killed all four children - Iraya, 12; Lillia, 10; Aidan, 6; and Dove, 1 - before taking his own life during the standoff.
Orlando police officers were called to the complex on Sunday evening by Lindsey's girlfriend, because of a domestic dispute, authorities said.
Four children and one man are dead after a 20-hour standoff between police and a suspect who had barricaded himself inside an apartment with the children on Monday.
A police spokeswoman said Tuesday that the medical examiner, as part of an investigation, would determine when the children were killed.
"It is a tragic ending to a night of horror", attorney Walter Benenati wrote on a GoFundMe page. He says Irayan loved video games and was an overachiever at school.
Mina said it was still unclear when the four children, two of whom belonged to suspect Gary Wayne Lindsey, 35, were shot to death.
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The girlfriend had called police late Sunday to report she had been beaten and she managed to get out of the apartment. The page can be found here. He was a felon on probation for arson among other charges.
Officer Valencia was seriously injured during the shootout and sent to hospital in critical condition. Two of them were Lindsey's and two were the girlfriend's, he said. The officer has undergone surgery but he has been unable to communicate, Mina said.
Lindsey was found dead in a closet when officers entered the apartment about 9 p.m., more than 21 hours after the standoff started, Mina said at a news conference just before midnight Monday.
"He killed himself and he killed the little kids", Jordanna said matter of factly.
"Losing four children is unfathomable", said Benenati, who added that the mother was in a state of shock.
Jackie Robinson said she had lived in the area for five years. Residents of the neighboring apartment complexes had to show identification and be escorted by the police.
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He came off as polite and friendly, neighbour Nicole Gonzalez said Tuesday morning as she returned to her Orlando home after being evacuated more than a day earlier during the standoff.
But Lopez said his interactions with Lindsey were "weird".
According to police records, Lindsey had been on felony probation at the time of the hostage incident after having pleaded no contest to charges of arson of a dwelling, willful fleeing or eluding law enforcement, and domestic battery, all of which stem from a 2008 incident involving a woman that Lindsey was in a relationship with.
The victim told police that Lindsey began stabbing a television set during an argument about a week before Christmas, and he ordered the woman out of the home before setting the building on fire using gasoline.
Sandi Marti and her wife, Carry, claimed that they saw flashes of light and heard three loud bangs Monday night. He was sentenced to 30 years supervision.
Almeida said he didn't know Lindsey personally but would see him wearing a gas mask and spray-painting items beside a tree outside his apartment building. "He didn't look like anyone who would cause trouble. These are people who would bring a tres leches, a flan to your house, you know, Heres a cake to eat", Benenati said. "You can't judge a book by its cover".
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