Hi Anissa,
I recently had this exact issue. In the flow, we used choices to define when to change the lead owner. So for example, if John Doe is you MDR, you could say to only change to John Doe if lead owner is empty (or whoever your default lead owner is.) Your default choice would then be to do nothing.
Let me know if there is something I can explain further. Also, please note that any notifications that are send to the MDR will now be sent to the lead owner.
Lauren