Take a look at this Google Street view of a laneway house that was built a number of years ago by laneway builder, Lanefab.
https://goo.gl/maps/ZCHd3NTWmjamuMeKA
I don't recall if the owner of Lanefab lives here or not, or if the owner of the house simply hired them to do the job, but if you take a look at the back of the house, there is a huge massive tree there. The laneway you see literally to the right of the main house sat a huge massive tree, similar to that of OP's example.
The tree had to be cut down in order to accommodate the laneway house. They definitely hired an arborist to do the job, and this was also when laneways were a hot thing to do (he was definitely the first in the neighborhood to do it.) Might be a chicken or the egg situation for OP. Best to consult a builder and/or arborist on this.