Upon completing one of the game's puzzles, and therefore unlocking its door, Chloe remarks "As a wise man once said, Abra goddamn kadabra." This is a reference to Sully, another character from the Uncharted series, and is a typical comment he would make.
During the Western Ghats section of the game Chloe Frazer says "Well I'll be go to Hell". This was one of Victor Sullivan's catchphrases in Uncharted 3: Drakes Deception (2011).
Uncharted: The Lost Legacy was originally supposed to be released as a DLC for Uncharted 4: A Thief's End, but later, the studio, Naughty Dog, decided to release it as a full stand-alone game
At several points during the adventure, Chloe refers to Nadine as 'china' - this is a common South Africanism meaning 'buddy', 'mate' or 'friend'. Nadine is South African so she would get it. The term stems from old Cockney rhyming slang, "china plate - mate", which was culturally adopted in South Africa.
At one point, Nathan Drake was considered to be a secondary character in the game but was dropped as Naughty Dog felt like there was nothing more to do with him.