I am travelling to Imir from BHX with Lufthansa and will change flights in Munich. Lufthansa have changed the Munich to Izmir flight to Sun Express, their partner airline. My question is - do I have to check my hold luggage in at BHX only, or will I have to check it in again from Munich to Izmir?
Barring places where you need to do customs declaration at an intermediate point of your journey (such as when your final leg is intra-US or intra-Japan) and barring connection times in excess of 24 hours, your luggage will be checked through to your final destination with almost absolute certainty.
In your case, having to recheck your luggage on a UK–MUC–Turkey itinerary would be exceedingly annoying as both check-in desks and luggage reclaim are landside of passport control; however, as you are transferring non-Schengen to non-Schengen there is no point in you entering the Schengen area for such a small thing. It would greatly disrupt operations and would make the connection much harder for those needing a visa to enter Schengen. So Lufthansa and Munich airport make sure that this type of trip can be done without rechecking.
Munich airport’s terminal two is basically one long concourse with two levels: a lower Schengen and an upper non-Schengen level with immigration checks at points where you can change levels. Coming from another EU country, you don’t need to go through any additional security, so you really just get dropped off in that long concourse and can immediately navigate your way to your departure gate. (The satellite terminal acts as little more than an extension to that long concourse connected to the rest in the middle still separating Schengen and non-Schengen.)
If either of your flights happen to arrive or depart from terminal 1 (I think I saw Sun Express depart from there at least once) that still doesn’t change the general picture as there is an airside connecting bus that connects the non-Schengen gates of T1 and the non-Schengen concourse of T2.