This anwer is just intended to give you some ideas.
The Cie lab, (actually any color space) is a 3d space.
I'm not sure on what is the "real" 3d space, becouse for practical reasons it can be converted into ortogonal coordinates, so you have 3 coordinates, not 2.
"Linear transitions" are relative to what road you take. To make transitions between colours you can take several aproaches.
This will give you diferent "Middle colours". In an HSB for example, the model 2 will mantain the Bright and saturation on the same level just rotating the Hue value. In terms of Hue it is a linear transition. But if you use another aproach the B and S values will be splited into 2 paths, like model 3, and that will not be linear.
On example No. 3 however, you don't cross diferent hue values, just the Origin and Target hue values.
Of course "linear transition"s is the obvius choice if you are using a mathematical aproach.
You can use some "S" curves or probably a logartimic curves, but, On what basis you choose each one? Probably you want a perceptual model?
At the end, a simple ((X2-X1)/2)+X1 will give you the middle value in X axis. The same for the y axis.