Kalman filter after lowpass filter: bad idea?
The Kalman filter is the optimal filter under various assumptions. You need to check whether those assumptions hold in your case:

a) the model perfectly matches the real system,
b) the entering noise is white and Gaussian and
c) the covariances of the noise are exactly known.

Without further detail I can't say whether your statement My experiments indicates that Kalman filter does not bring anything interesting after LP filtering. is true or not.
Use Occam's Razor: the simplest approach that works is the best. That is, it may well be that for your situation a low pass filter is all you need.