As I said earlier, DOF is a function of subject distance, focal length equivalent and physical aperture opening.
The LX7 has a lens that, at full tele, has a focal length of 17.7mm and an aperture of f/2.3. It's true that it has a somewhat longer equivalent focal length (90mm) than the 50/1.4 on either full frame or APS-C bodies. However, the physical aperture opening is only 17.7 / 2.3 = 7.69mm, instead of the >35mm physical aperture opening of the 50/1.4 lens; that's a huge difference. As I said earlier, it's not the f-number that counts; f-numbers are useful for calculating exposure, but in and of themselves, they tell you nothing about DOF.
[edit] yes, what you say in your latest post is correct, provided the 35mm lens doesn't have a full stop faster lens (for instance, a 35/1.0 lens would have a ~35mm physical aperture opening just like the 50/1.4 lens, and since the field of view is the same too, they'd have the same DOF).