Difference between LASSO penalty in neural network and just LASSO regression
I think Lasso Regression, is a type of regression model which implements the lasso penalty (L1 regularization) within its algorithm (different from normal regression algorithms).

Lasso penalty is more of a generalized penalty that can be put on any learning algorithm. 

The concept behind both ideas are the same, but their area of implementation is different.

Hope this helps !!