The Lord God, Adonai, is our Lord, our Sovereign King. God is the Lord of Lords and the King of Kings. Adonai is used throughout the Old Testament, as people relate to God, and declare His goodness. It is the name use as people pray to God in earnest need and seek help from our almighty God.
2 Samuel 7:18-22
Then King David went in and sat before the LORD [Yahweh]; and he said: “Who am I, O Lord [Adonai] GOD [Yahweh]? And what is my house, that You have brought me this far? And yet this was a small thing in Your sight, O Lord [Adonai] GOD [Yahweh]; and You have also spoken of Your servant’s house for a great while to come. Is this the manner of man, O Lord [Adonai] GOD [Yahweh]? Now what more can David say to You? For You, Lord [Adonai] GOD [Yahweh], know Your servant. For Your word’s sake, and according to Your own heart, You have done all these great things, to make Your servant know them. Therefore You are great, O Lord [Adonai] GOD [Yahweh]. For there is none like You, nor is there any God [Elohim] besides You, according to all that we have heard with our ears.

When David (as well as many others throughout scripture) went to the LORD in prayer, he addressed Him as Lord God, Adonai Yahweh. He is saying, you are the one and only, self-existent, sovereign Lord. God is great and awesome. He has done so much for us. He is a God who loves us and seeks an intimate relationship with us. It is always good to remind ourselves of who God is and what He has done for us. We see this throughout the Psalms and prayers in the Bible from those who follow Him.
Psalms 86:1-15
A Prayer of David.
Bow down Your ear, O LORD [Yahweh], hear me; for I am poor and needy. Preserve my life, for I am holy; You are my God [Elohay]; save Your servant who trusts in You! Be merciful to me, O Lord [Adonai], for I cry to You all day long. Rejoice the soul of Your servant, for to You, O Lord [Adonai], I lift up my soul. For You, Lord [Adonai], are good, and ready to forgive, and abundant in mercy to all those who call upon You.
Give ear, O LORD [Yahweh], to my prayer; and attend to the voice of my supplications. In the day of my trouble I will call upon You, for You will answer me. Among the gods there is none like You, O Lord [Adonai]; nor are there any works like Your works. All nations whom You have made shall come and worship before You, O Lord [Adonai], and shall glorify Your name. For You are great, and do wondrous things; You alone are God [Elohim].
Teach me Your way, O LORD [Yahweh]; I will walk in Your truth; unite my heart to fear Your name. I will praise You, O Lord [Adonai] my God [Elohay], with all my heart, and I will glorify Your name forevermore. For great is Your mercy toward me, and You have delivered my soul from the depths of Sheol. O God [Elohim], the proud have risen against me, and a mob of violent men have sought my life, and have not set You before them. But You, O Lord [Adonai] , are a God [El] full of compassion, and gracious, longsuffering and abundant in mercy and truth.

As we cry out to the Lord, whether in our distress or in our joy, ought to acknowledge Him for who He is and what He has done. I think as we call upon the Lord, as we praise His name, as we describe Him as best we can of who He is, it helps us to remember that He is a God who willing and able to answer our prayers. He is the God who makes all things good no matter how bad the circumstance may be at the present time. He has already done so much for us by sending His one and only Son to pay for our sins. Jesus died on the cross and was raised from the dead to declare victory over death and sin, and because of this we can declare it too!
Isaiah 7:14-15
Therefore the Lord [Adonai] Himself will give you a sign: Behold, the virgin shall conceive and bear a Son, and shall call His name Immanuel [God with us]. Curds and honey He shall eat, that He may know to refuse the evil and choose the good.
And the Lord, our Lord, keeps His word. When He says it will happen, it does. When He says He will bless us, He will. When He says He will provide a way to salvation, He did. Jesus came in the flesh and paid for our sins. He is “God With Us.”

Matthew 1:20-23
But while he thought about these things, behold, an angel of the Lord appeared to him in a dream, saying, “Joseph, son of David, do not be afraid to take to you Mary your wife, for that which is conceived in her is of the Holy Spirit. And she will bring forth a Son, and you shall call His name JESUS, for He will save His people from their sins.” So all this was done that it might be fulfilled which was spoken by the Lord through the prophet, saying: “BEHOLD, THE VIRGIN SHALL BE WITH CHILD, AND BEAR A SON, AND THEY SHALL CALL HIS NAME IMMANUEL,” which is translated, “God with us.”
Adonai is the God who wants an intimate relationship with us. He is our Lord who answers our prayers. He is full of mercy and grace, compassion and truth. He is our Deliverer. He is all that we need. He is our God.