iPhone 6 recognizing my External lavalier mic as an headphone not microphone
It would be helpful for you to include the make and model of the mic that you are using, as anything we say will be nothing more than a guess.

That said, if you compare a pair of generic earbuds with Apple's earbuds you will find that there are more "rings" around the shaft of the Apple earbuds than the generic ones you get elsewhere.

One of the "extra" rings is for the mic. And to match up with the iPhone the microphone "ring" needs to be in the exact same place the iPhone's jack expects it.

Which leads me to what I think might be your problem:

Unless your mic specifically says "iPhone compatible" it is likely that the plug on the end of your mic does not have the connectors in the right place for the phone to recognize your mic as a microphone.

And when you get down to it a microphone can be thought of as a specialized speaker, which it is. Hence the reason you can play sound out of it now.

So what do you do about this?

There are options. You could return it and get a mic that specifically says it works with an iPhone. You could contact the manufacturer and see if they have an adapter that would do the same thing with your current mic.

Also if it IS specifically compatible with your iPhone then it is not working and should be returned for replacement, if possible.

If you edit your original question and add the make and model of the microphone we might have better guesses.