This is the only time Scripture clearly says something about "living for God." Here it means "we live because of God." It does not mean "we live for the purpose of attempting to please God" nor "we live on behalf of God." When scripture says that Jesus died "for us" the word used indicates that He died "on our behalf." Even if we take "for" to mean something else than "because of" the scripture clearly says "if we live, we live for the Lord." The condition is being alive. The condition is not our behavior. We cannot try to live for God because, if we are alive, we already do. You always live for God because He is your life, He always lives for you, you live because of Him.
"For you have died and your life is hidden with Christ in God. Christ is your life." (Colossians 3:3-4)
Saying "I live for God" is like saying "My heart and brains live for me." Without them there is no life. Without God there is no life. When we say we live for God we separate Him from ourselves. The truth is He is in us and we are in Him. The same ideas go for our own self-efforts. "I try to live for God." Is like saying "My heart tries to live for me but sometimes the dumb thing just don't work right." You are either alive or you are dead. If you are alive your heart is living for you and if you are alive you are living for God.
"Jesus died for all. He died so the living would no longer live life alone but with Him who died for them and rose up for them." (2 Corinthians 5:15)