As was mentioned, there doesn't seem to be anywhere for another lane to take traffic. (building in question is the rectangle coloured red).
There's already a dedicated turn lane that takes traffic onto Memorial in a West direction. If a second turn lane was created, there's no lane on Memorial for it to merge into, and adding another lane to Memorial likely wouldn't ever fly as it would either take out several blocks of houses/apartment buildings in Sunnyside or take out the bike paths on the other side. Adding a new turn lane so that all 4 lanes can come south also wouldn't work as the Langevin bridge is only 2 lanes. In theory if a new 3-4 lane bridge was built then a new turning lane would be useful, but with the empty land south of the Bud's furniture store I don't see why adding that lane would require demolition. I suspect there does exist in some old study a future plan to demolish the building, but I believe way the situation is on the ground today that it would not happen.
Now if there was a plan to demolish for some other reason...
I'll ask the City about this.