Is it permissible to lie to a father who prevents his observant son from associating with religious people and attending religious lessons, fearing for him from arrest?

If going to places that the father prohibits is necessary, then there is no objection to it, and one should use ma'areedh (indirect speech or equivocation), because the father does not have the right to prohibit necessities. However, if going is not necessary, then obedience to parents is obligatory, especially if they have a valid reason for the prohibition.