Is it permissible to supplicate for and give charity on behalf of my mother, who sometimes prayed and sometimes abandoned prayer?

There are two categories of those who abandon prayer out of laziness: one who abandons it completely, who is a disbeliever and outside the fold of Islam; and one who abandons it sometimes and prays sometimes, who is a sinful Muslim deserving of the threat [of punishment]. If your mother falls into the second category, then strive in supplication and seeking forgiveness for her.