The phrase "drive a horse into a lather" means to push or force a horse to the point of exhaustion or agitation. There are several synonyms for this phrase, including "whip up," "work up," "roil," "provoke," and "incite." These words all suggest a level of agitation or frustration that can be achieved by overworking or pushing too hard. In some cases, these synonyms may also suggest a sense of anger or irritation on the part of the person doing the driving, adding a layer of emotion to the phrase. Ultimately, no matter which synonym is used, the goal is to convey a sense of intensity and discomfort for the horse being driven.