Looking at the plan and profile of the tunnel in Exhibit 4-18l (page 102 of the PDF) of the
2017 EPR report the top of the tunnel at Lawrence is 135 metres above sea level (ASL) with ground surface about 157 metres ASL. That would be closer to 10 stories than 20 stories. Deep sure, but compare to some of the Relief line stations.
The new platforms for Pape station have a ground surface of 115 metres above the top of the new tunnel at 92 metres - which is not only the same depth, but the tunnel is designed as cut-and-cover (north of Cavell Avenue).
And Gerrard station has a ground surface of 90 metres above the top of (bored) tunnel at 54 metres above sea level. Which is significantly deeper.
Given the comparable depths, particularly for the DRL cut-and-cover construction at Danforth I'm not sure what in particular precludes technically installing a station at Lawrence East on the SSE years later. (other than the closure). The profile through Lawrence is relatively flat, certainly no more of a slope than proposed for some DRL stations - in fact, just north of Lawrence closer to the hospital, it looks very flat! Ideally the station would be built at the same time - but nothing precludes starting construction on the current schedule, and adding a project to at least rough in the station box, so as to avoid a lengthy future closure.
The text of the report clearly states on 36 (Section 4.2.2) that "
The vertical and horizontal profile in the vicinity of McGowan Road and Lawrence Avenue East, will meet those required for the possible construction of a Lawrence East Station in the future".
There's no mention I see in the text of the EPR report, but looking at the plan and profile, there's a relatively flat, straight section that looks suitable, from the intersection of Brimely and Eglinton, westward.