The money was believed to be from unlawful activity, but no arrests have as yet been made, the agency added.
This is the latest in a series of raids which uncovered bundles of cash in Nigeria, Africa's biggest economy.
In March, the agency said it had found "crispy" banknotes worth $155,000 (£130,000) at the airport in northern Kaduna city.
Apart from US notes worth $43.4m, investigators found nearly £27,800 and some 23m naira ($75,000) at the four-bedroom flat in Lagos's affluent Ikoyi area, the Economic and Financial Crimes Commission (EFCC) said in a statement.
The "neatly arranged" cash was stashed in "sealed wrappers" in wardrobes and cabinets in the seventh-floor flat, the EFCC added.
Guards told investigators that no-one lived in the flat, but a source reported that a "woman usually appeared on different occasions with Ghana Must Go bags", the EFCC said.
"She comes looking haggard, with dirty clothes but her skin didn't quite match her outward appearance, perhaps a disguise," it quoted a source as saying.
