Uhhhh, bad news: no such thing as far as I know, certainly nothing in your budget range. Lavaliers still pick up plenty of background sounds – so would any mic. You could maybe try hanging a very directional shotgun microphone off a mic stand just out of frame – at your budget level you would be looking at renting the audio gear you need not buying.
If you record a few seconds of “silence” at the start of each sound clip you may be able to use that noise profile in an audio editing program to help remove some of the background noise during post production but really the simple answer is “don’t do the interview there” – you can always film b-roll there for a little color. In fact, it’s a cool technique when filming an interview with someone who works with machines, computers etc to film them separately interacting as they work and then use that as B-roll while continuing the interview audio and then switching back to the primary interview location without a break in the interview audio.
I never do this myself but I guess you could film the subject in a quieter environment in front of a green screen and then composite in the original noisy location in post but that’s a lot of work and can look fake. This way you could record the machine room sounds separately onto another track in your video track and have very precise control of the background sounds.
Steve Crow
Crow Digital Media
http://www.CrowDigitalMedia.com