The February 7 1946 edition of the Toronto Daily Star contained this brief article about a property dispute in Leaside:
I looked up the 1948 Toronto city directory, as I figured that the building would be built by then, and it was: the Leaside Press was listed at 219 Randolph Road, with Arthur E. Donahue as its proprietor. I was curious as to whether the building wound up being built with its entrance at the side or the back, but Google Street View revealed that the building is long since gone – there are now condominiums on the corner of Randolph and McRae. The west side of Randolph Road does appear to be completely residential, though.
The Leaside Press changed its name to the Leaside Advertiser in 1950. The latest directory that I can access online, the 1969 directory, still listed the Leaside Advertiser at 219 Randolph, with Mr. Donahue still in charge. This 2013 page from the Toronto Public Library states that the Leaside Advertiser remained in existence until about 1999.