Q-M242 is the parent to all other Q branches. Its parent is P-M45. YFull dates show that Q-M242 is between 34,000 and 29,800 years old (95% CI). This is a much older date than in older published studies, and perhaps helps explain the great geographic spread of the branches under it.
Lima is the capital city of Peru in South America. It is unsurprising then that the 1000 Genomes project found a Q sample there. Sample HG01944 from that project though does not seem to belong in South America. You see, it is Q-M120, and that is an East Asian lineage.