You’re Axle to Crown height is going to increase by at least 40mm, possibly upto 70mm) as the Lyricks, for a similar travel, have a longer A2C. Moving to a 650b will add around 20mm A2C on it’s own. You’re likely to raise your BB height by 20-30mm.
As others have pointed out, fitting longer forks will lift your bottom bracket. I don’t know how feasible it is to fit an offset bushing to compensate, but even then you may end up with a taller BB than you started out with.