Why does the 23rd Psalm (“Mizmor l’David Hashem Ro’i lo echsar”/ “The Lord is my Shepherd…”) begin by speaking ABOUT the Lord by using the term "He" but later addresses the Lord directly by using the term "Thou"?

The dual relationship which we have with God is that he is also our Father (Avinu) and also our King (Malkenu). The first is the aspect of closeness which stresses the attribute of kindness (God’s 4 letter Name), while the second stresses the attribute of justice (the name Elohim, literally: Judge). God is both approachable (“And you shall love your God”, Dvarim 6, 5) and He even allows us to approach him in second person (Thou/You), yet also Judging and deterring us from doing bad (“The Lord your God you should fear”, ibid, 13), where we speak to Him in third person (He), out of respect. It is actually very common to have both together to stress the Unity of both aspects, and in fact many of our blessings (brachot) throughout the day, purposely start with “You”, but end with “He”, [e.g.: Baruch ata (Thou/You) Hashem shehakel nihiya bdvaro (with His word)]. Both aspects of our relationship with Him are very true and both are very important and necessary. Chag Same’ach!