Besides the 416 you have you might want an 816 for outside work. The tighter pattern gives you a little more flexibility in mic placement in noisy situations. Lavaliers can have a noise advantage over booms because of proximity to the sound you want to record. If you are using wireless Lavs check the settings (if yours has some) on the transmitter. Some transmitters can be fine tuned to have less ambience picked up. If there are intermittent sounds there is not much you can do but ask for another take. Record lots of room tone. Some mixers have better equalization than others and this can help make extraneous nose tolerable. If the director doesn't want or can't to give the sound department any help then ADR might be the only solution.