regarding speed - the Bloor Line between Kipling and Keele takes 13 minutes to go 6.7km with an average stop spacing of ~850 metres - the same stop spacing as the underground part of the Crosstown. This is an average speed of 31km/h.
Eglinton's underground speed should be generally similar. Which means the travel time for the 11km underground portion should be ~21 minutes.
To hit that 38 minute travel time, it means that the LRT would need to cover the ~8km surface portion in 17 minutes, or an average speed of 28km/h. I'm doubtful it'll be hit.
The western half of the surface portion will be relatively quick. There are just 5 signalized intersections from Laird to Victoria Park, across about 5km, and average stop spacing remains at about ~850m. Speed across here should be relatively strong - I could see 25km/h or greater. So lets assume 11 minutes to get to Victoria Park from Leaside, which leaves.. 6 minutes to get across the Golden Mile. There are 8 signalized intersections and 6 stations across 3km. This part will be SLOW. Probably like 20km/h, if that. Optimistically, probably another 9 minutes to cross that 3 km.
Total estimate travel time: ~41 minutes.
Also: The Lebovic stop still bothers the hell out of me. It's completely unnecessary.