Why the estimated Lasso coefficients of almost all variables are equal to zero?
This was due to the fact that I should normalize my data before passing it into the algorithm. For example,

scaler = StandardScaler()
scaler.fit(X_train)
X_train = scaler.transform(X_train)
X_test = scaler.transform(X_test)


Or, the "normalize" parameter of Lasso should be set as True. 

Lasso(alpha=float(alpha), normalize=True, random_state=42)