Well, I wasn't yet able to completely nail down the pre-LaSalle history of the site to figure out where the "Switch List" name comes from. But, here's a bit of info I was able to dig up so far from the 1875 Compton & Dry Topographical Survey.
Apparently the building at the corner of Olive and Broadway wasn't notable enough to make it on the legend. It's located between structures 73 and 74. It appears to be a small shop or business of some type.
Version 1 of the Mercantile Library is noted as structure 71, for reference. It was rebuilt in the 1890's as a taller, fireproof structure (Version 2), and then re-clad in the 1950's (Version 2.5). You can even see the signage on the side of the building in this drawing.
Structure 73 is the Evening Journal (which is technically part of Hotel Indigo now - the building that housed Paradowski Creative - 303 North Broadway). Structure 74 had a few tenants, but I think this is west of the LaSalle footprint.
Lastly, I believe the building in question can also be seen in the very last photo below, at the very far-left. I'm sure there are more images out there showing this corner a bit better. The Missouri Historical Society website is usually pretty handy, but the search function doesn't appear to be working for me at the moment.
As a fun aside, Henry Shaw's house is structure 81 - what is now the parking lot behind the Union Trust building.