Hi Alex,
Looking at this phrase and I'm thinking it is critical that a comma be put in the right place for it to read right. So here it is in the NKJV, makes a difference.
Isa 51:22 Thus says your Lord, The LORD and your God, Who pleads the cause of His people: "See, I have taken out of your hand The cup of trembling, The dregs of the cup of My fury; You shall no longer drink it.
Isa 51:22 ThusH3541 saithH559 thy LordH113 the LORD,H3068 and thy GodH430 that pleadeth the causeH7378 of his people,H5971...
The first part "thus says your Lord," is saying who is speaking, then the second part "The LORD and your God," is giving the title of who is speaking. The phrase the LORD your God is used many time, without the 'and' in there, which I don't think makes much difference. There are a few more places those words are used like that.
Isa 3:1 For behold, the Lord, the LORD of hosts, Takes away from Jerusalem... (NKJV)
Isa 1:24 Therefore the Lord says, The LORD of hosts, the Mighty One of Israel, "Ah, I will rid Myself of My adversaries, And take vengeance on My enemies. (NKJV)
I found another place where those same Hebrew words were used in that same order, but without the "and your" in Exodus.
Exo 34:23 "Three times in the year all your men shall appear before the Lord, the LORD God of Israel. (NKJV)
Exo 34:23 ThriceH7969 H6471 in the yearH8141 shall allH3605 your men childrenH2138 appearH7200 (H853) beforeH6440 the LordH113 GOD,H3068 the GodH430 of Israel.H3478
And here is another place you can see how these words can be used together.
Deu 10:17 For Jehovah your God is God of gods, and Lord of lords, a great God, the mighty, and a terrible God, who does not respect persons nor take a bribe. (NKJV)
Deu 10:17 ForH3588 the LORDH3068 your GodH430 is GodH430 of gods,H430 and LordH113 of lords,H113 a greatH1419 God,H410 a mighty,H1368 and a terrible,H3372 whichH834 regardethH5375 notH3808 persons,H6440 norH3808 takethH3947 reward:H7810
Anyway hope that helped.
mercy, peace and love
Kat