How can I know If LASSO logistic regression model is good enough to be feature selection tool? It is known that LASSO can be used for feature selection.
How can I know if the model is reliable for that purpose?
In general the model's accuracy, R squared and etc, don't bother me because I don't use it for prediction.
But for example, if the model's accuracy is 0.5, is it a good idea to use it for dropping variables?
(After the feature selection process, I will choose a classification model and train it on the data, and in that step, the predictor accuracy is important for me)

Lasso is a common regression technique for variable selection and regularization. By defining many cross validation folds and playing with different values of $\alpha$, you can find the best set of beta coefficients which confidently predicts your outcome without overfitting or underfitting. If the Lasso technique has assigned the beta coefficient of any covariates to 0, you can either chose to drop these features since they do not contribute to the predictor or proceed in the knowledge that those covariates are essentially meaningless.
As such, consider a sample consisting of N observations, each with p covariates and a single outcome (typically the case for most regression problems). Essentially the objective of Lasso is to solve:
$ \min_{ \beta_0, \beta } \left\{ \sum_{i=1}^N (y_i - \beta_0 - x_i^T \beta)^2 \right\} \text{ subject to } \sum_{j=1}^p |\beta_j| \leq \alpha.
$
Here $ \beta_0 $ is the constant coefficient, $ \beta:=(\beta_1,\beta_2,\ldots, \beta_p)$ is the coefficient vector, and $\alpha$ is a prespecified free parameter that determines the degree of regularization.
