regarding lasso.score in lasso modeling using scikit-learn
R^2 is a statistical measure of how close the data are to the fitted regression line. It does this by seeing percentage of the variance of dependent varible that's explained by independent variable.
To know more about R^2 score refer this video.
So, basically it is a metric to see how well model fits the data but it is not adequate.
Refer this discussion on why R^2 score is not good for Lasso.