From my own experience, there are certain avenues for legal assistance, however organizations do change; e.g. one organization, Milah, that offers help for Olim and used to have a lawyer volunteer a few hours a week, no longer has this service.
The Revacha ( רווחה ) which means welfare, is situated in most neighbourhoods (Shchunot שכונה). Most of them have certain hours of legal assistance. To the best of my knowledge one is required to meet with the social worker prior to booking an appointment with the lawyer, but this could be different for the different branches. It is worth asking at your local Revacha office.
Depending on the nature of the legal assistance, the organization for the country you made aliya from (e.g. UJIA, AACI) sometimes knows lawyers who will help an Oleh as a one off depending on the nature of assistance required. Once again, it is worth asking.
I posed this question to Tzvi Szanjnburn, one of our guest writers who is a lawyer. Here is his answer:
The Ministry of Absorption does not provide any free legal aid. Depending on your income, and the type of legal help you may need, there are public defenders in the Ministry of Justice, who will provide you with free legal aid. There are other organizations that provide free legal help, including the Israeli Bar Association and our organization as well (WWW.VOLEH.ORG).
Sincerely, Tzvi Szajnbrum, Esquire.