The placement of good in this sentence is tricky. One might expect to see “my good lord” instead – but no – it’s – Nay, good my lord.
And I THINK the “good” in this sentence is doing the same thing no matter where you put it but thinking about putting it before “my” has the effect of emphasizing the “good.” It maybe makes the plea even stronger.
I know a lot of actors who are not diligent about text and word order. They’re happy to just get across the idea. Which you could do if you slipped up and said “my good lord” but I think you miss the opportunity to really feel what the line is doing in that case. It’s small but interesting.