I could have given you a lift.

This sentence is an offer only in theory. In practice it expresses possibility. Note that this is the main clauseA clause that could be a sentence in itself. E.g.: I wouldn’t go there if I were you. ("I wouldn't go there") When I arrived he was surfing. ("he was surfing") of a third conditional sentence. 

To express offers, usually the auxiliariesA helping verb used with main verbs to express mood, voice and tense. E.g.: I can't stand when I am disturbed. ("can", "am") of permission, possibility, suggestion and willingness are used.