Lasso Regression Assumptions These are the linear regression assumptions:

Linearity: The relationship between X and the mean of Y is linear.
Homoscedasticity: The variance of residual is the same for any value of X.
Independence: Observations are independent of each other.
Normality: For any fixed value of X, Y is normally distributed.

Do they apply to Lasso Regression, too?

Yes, they are valid also for Lasso, Ridge Regression and Elastic Net. I think you are referring to classical linear model (CLM) assumptions for cross-sectional regression:

*

*Linear in Parameters

*Random Sampling

*No perfect collinearity

*Zero Conditional Mean

*Homoskedasticity

where the first four are used to establish unbiasedness of OLS, whereas the fifth is employed to derive the usual variance formulas and to conclude that OLS is Best linear unbiased.
One can also assume normality of the error term to obtain the exact sampling distribution of t statistics and F statistics, so that one can carry out exact hypotheses tests, but normality is not a necessary assumption for CLM.
