Lasso regression in python with differential penalties
Your problem is very specific, people usually don't train models like this, that's why there's nothing like that in sklearn. It's even incorrect to call lasso regression, but that's a question of terminology. But you can actually write the subdifferential of this loss and write subgradient descent yourself in python.
I want to use Lasso regression in order learn a coefficient matrix, B. The problem I'm trying to solve is:

min{||y-xB|| +lambda{P X B}_1}

Where P is some penalty matrix: P_ij gives B_ij penalty p (the bigger P_ij the smaller B_ij)
How can I do this using python (didn't find anything useful in sklearn)?