How to set up live audio feed (with lavalier mic)? I've been performing live video broadcast for awhile now carrying around lots of equipment so I can have nice live audio feed in the video stream but I'm currently looking for ways to simplify my setup.

I'm using a full blown mic on a stand connected directly to an audio interface with XLR cable in between which works fine but it's not very mobile and it's not very convenient for the person talking as they will have to stay close to the microphone without being able to move away from it.

I would like to have something more flexible instead like a lavalier mic or a headset mic (the person talking is not in the camera view so they don't have to look nice) that would allow the speaker to move around and have more freedom and still be able to use this setup without a pause for a long periods of time (sometimes over 4-5 hours). From what I've seen online, I'm not even sure that if I can and how to connect a lavalier mic (or nice head set) for live audio feed and even if I find a way to do so - what would be a good recommendation to have "infinite" power source for the mic as batteries would not hold long enough for some of the sessions that I have. Would it work with any model or only some specific ones would be suited for this setup? Any tips, information or recommendations are welcome. Thank you!
First thing is to check whether your audio interface XLR input can supply 48 V phantom power. If the answer is yes, look for a microphone that can be powered by phantom power. If this is not the case, look for an adapter that can power your mic and output to your XLR input.

For your use case, I think that a headset mic would be better than a lavalier one as it maintains the same sound when the speaker moves his head relatively to it's torso. You also are more safe against clothes noise. Most serious microphone makers offer this kind of product. Entry level products can be found from around 100 €.