I used cross validation to select lambda. Then I performed lasso and get non zero coefficients (features). Shall I perform cross validation for these non zero coefficients as a kind of validation?
(Just guessing what you are actually asking)
Shall I perform cross validation for these non zero coefficients as a kind of validation
The final model (with the LASSO-determined coefficients) needs to have its own validation with a set of completely unknown cases in order to get a good estimate of its performance.
That is, if you do a cross validation for this final model validation step, you need to need to wrap another "outer" cross validation around all calculations that lead to the LASSO-model (including the "inner" cross validation you used for tuning of $\lambda$).
This is known and discussed here under the name of double cross validation or nested cross validation - it is a resampling version of the splitting into training-tuning-final model validation (aka test) method.