Is it permissible to lie to one's family by claiming to be delayed at work, for the purpose of going out for recreation?

It is not permissible for you to lie explicitly to your family. The legitimate way out is to inform them directly of your need to go out, or to resort to using allusions (ma'areedh), which means using a word that has a double meaning, from which the listener understands something other than what you intend. Lying is forbidden except for reconciliation, war, or to one's wife. If it is possible to use allusions, then lying becomes forbidden. Allusions are permissible when there is a need for them and are disliked when there is no need.