I generally do not take cases that I do not believe in. About 80% of my cases are taken on a contingency and if I do not win, I stand to lose a fairly significant sum of money. (Doctors charge about $2,500/hr to testify with a 4 hour minimum.) Of course, there are instances when you come to discover that your client has not been forthright with you. My approach to these situations is to have a come to Jesus talk with the client. I tell them if I can smell a lie, so will the other attorney and so will the trier of fact. If statement that I think is not truthful does not completely eviscerate their case, I advise them to be truthful and explain the discrepancy. If the misrepresentation is one that goes to the heart of the matter, then I cannot solicit the lie in court.
Keep in mind, generally I do not know that client is lying. My spidey sense just tingles. Most times, the client is not "lying" they just believe they are right and have a crappy case. Sometimes those clients force you to trial with a loser. You do the best you can within your ethical confines and present the case. Usually, the jury gets it right.