I have no problem with people saying they have “accepted Jesus as Savior or Lord” or praying that others might do the same.
True, Jesus is Lord whether acknowledged by us or not. The only significant acknowledgement is that of the Father, and Jesus does carry that imprimatur. Peter makes this clear in his sermon at Pentecost.
“Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified.” (Acts 2:36)
Someone “accepting” Jesus as such does not make Him what He already is. But it does do this… Accepting Jesus voices a person’s expressed recognition of Jesus as the Christ and that person’s personal declaration of changed relationship to Him. It is another way of confessing Christ (Phil. 2:9-11), another way of obeying the command of the Father to believe on His Son (1 John 3:23).
There are technical ways of expressing things and there are colloquial ways. To-may-toe, to-mah-toe. The crucial element in it all is saving faith, present as a gift of God through the work of the Spirit. The vocabulary of saving faith may be simple or scholarly but the language is the same, the language of reciprocal love to Him who first loved us.
What is non-negotiable in accepting Jesus as Lord and Savior is a word we noted above—change. To embrace Jesus as Savior is to renounce our own ability to save ourselves, to disavow anything we could do to save ourselves. To accept Jesus as Lord is to relinquish our own lordship, abdicating the throne to Him, seeking His will, serving His kingdom. We defer to Jesus in each of these areas. (I might note that it is unacceptable to accept Jesus as Savior without accepting Him as Lord. To embrace a Christ who is Savior but not Lord is to embrace a different Christ than that of the Bible.)
Change is vital to saving faith. We repent and believe. Faith and repentance are two sides of the same coin. We come to Christ in believing repentance. We align ourselves with Him in repentant faith. We live daily in Christ in the same way, denying ourselves to follow Jesus (Luke 9:23). He must increase; we must decrease.
Some cringe at the expression of “inviting Jesus into our hearts.” We might quibble on technical terms, like a scientist might demur at the thought of the “sun rising.” Technically, the sun stays the same. It is the earth that rotates to reveal the sun’s presence and glory.
In similar fashion, whatever words we use to express the glory of the risen Son proceed from hearts that have been already been occupied by Him.