Close friend Kareen El Beyrouty said: "They are lovely boys and have been through hell to get here".
It comes as angry protesters gathered, demanding answers over the tragedy.
Syrian refugee Mohammed Alhajali, a civil engineering student who wanted to help rebuild his war-torn homeland one day, was the first victim named.
Mr Alhajali's older brother Omar - who was with him in the flat - survived the fire after they were separated on the way out.
She had no phone to call for help in the early hours of Tuesday morning, which is why she had taken to Facebook, said Lammy.
He wrote: "May you rest in peace Khadija Saye".
Her latest work, which is now on display at the Diaspora Pavilion in Venice, "explores the migration of traditional Gambian spiritual practices and the deep rooted urge to find solace within a higher power". Her work is on display at the 57th Venice Biennale.
Illegal Telephone Exchanges, Allegedly Used To Spy On India, Busted In Maharashtra
As per Telecommunication Department officials, these illegal exchanges have caused a revenue loss of ₹15 crore to the country. Total 64 Sim cards, one laptop, two unauthorised global gateway machines and other material were recovered from him.
Becoming emotional, he said: "And it breaks my heart, that it's happening in Britain in 2017".
Appearing on Channel 4 News, Lammy said: "She was a young black woman making her way in this country".
David Lammy said "people should be held to account" after the deadly fire killed 17 in the Latimer Road block of flats.
The death toll now lies at 17 but many people remain missing.
He said that efforts were focused on keeping families as informed as soon as possible when they know beyond doubt that it is their loved one who has been identified. There's a fire in my council block.
Friend Ariana Neumann Rodger posted on Facebook that 22-year-old son, Farhad, was being treated in hospital while his mother was in intensive care at Kings College Hospital. He had last been seen escaping the blaze with neighbours and family, but reportedly got lost in the smoke. Among the missing are Jessica Urbano Ramirez, 12, Mariem Elgwahry, 27, who lived on the 19 floor and Tony Disson, 66, who lived on the 22 floor. They are believed to be Marco Gottardi and his girlfriend, Gloria Trevisan, based on information from Gottardi's cousin. The pair had made final phone calls to relatives as the flames closed in on their flat.
Farah Hamdan and her six-month-old child, pictured left, are reported missing; and, pictured right, one of her two daughters reportedly found in hospital.