Explanation
Yes. The name Ontario was used for the lake long before it became the official name of the Canadian province in 1867.
A French map dated to 1660–1669 labels the body of water “Lac Ontario ou des Iroquois.” More than two centuries later, sections 5 and 6 of the Constitution Act, 1867 named Ontario as one of Canada's four provinces and made the former Upper Canada the Province of Ontario.
The exact Indigenous-language origin and earliest surviving written use of Ontario are discussed differently across historical sources. That uncertainty does not affect the chronology: documentary evidence places the name on the lake by the 17th century, well before the province was created.
Key takeaway
Lake Ontario carried the name Ontario more than two centuries before the Province of Ontario was established in 1867.