Again, I know street name changes were fairly common, and I'm not expecting the name to be found on street signs. But if the road had originally been called Lakeshore, why would it not be mentioned on Wikipedia, for instance? The names of the streets that make up today's Dundas are not exactly difficult to find.
The best bet for producing a primary source that confirms the original name would be to investigate old maps through the TPL's digital archive, but it seems to be throwing back a 403 error. The city of Toronto only has one post 1919 fire insurance map, where neither a Lakeshore nor a Queens Quay exists, there seems to be some kind of access road called Lake Street that went as far as John Street. I have several old transit maps which were created in the 1970s by historian John Bromley, which otherwise make reference to former street names where appropriate, that refer to the street as Queens Quay going as far back as 1936, which I consider reliable as a secondary source.
Click on any map area to see a more detailed plan.
www.toronto.ca
Aha, here we go. Two maps, from the World War I era, by the Toronto Harbour Commissioners, showing the proposed development of the waterfront, with Queens Quay being the name of the street. As a primary source, I don't think you can get much better than this.