Here's what I know about that. Please note the definition of "acknowledge" (confess) near the bottom of the post. Thanks.
Anyone who has knees to bow and a tongue to speak, in heaven and on earth and under the earth (in the realm of the dead), will whole-heartedly, and without reservation, acknowledge that Jesus Christ is Lord.
When we meet with God after death they will see him as he is; King of Kings and Lord of Lords.
Non Christians will know him and be able to see him face to face. They will have no choice but to acknowledge who he is, and that they had been wrong.
That does not mean that they will be able to confess their sins, repent and ask for eternal life. They will know that Jesus was Saviour of the world, but he hadn't been their Saviour.
Paul says, "we live by faith, not by sight", 2 Corinthians 5:7.
Have a look at Hebrews 11 to see how God values faith and those who live by faith.
When people see Jesus after death there will be no need for faith - he will be right there, in all his glory.
No one can say that “Jesus is Lord,” except by the Holy Spirit.
In this life; no, we can't.
It takes faith to believe in and accept Jesus, and submission to be able to declare him as Lord.
If you declare with your mouth, “Jesus is Lord,” you will be saved.
In this life; yes.
It does not say, that everyone who has failed to receive Christ by faith in this life will be able to do so after they die - when they will see him face to face and need no faith to believe that he exists.
I don't see any verses in Scripture that say, "repent and believe - if you want to. But if you don't, that's fine; you will be able to do so after you die, and still receive eternal life."
Note on "acknowledge" in Philippians 2:11 from Strong's Concordance
S1843 eksomologéō (from 1537 /ek, "wholly out from," intensifying 3670 /homologéō, "say the same thing about") – properly, fully agree and to acknowledge that agreement openly (whole-heartedly); hence, to confess ("openly declare"), without reservation (no holding back).
Of course people will be able to acknowledge, confess, agree who Christ is when they see him face to face in all his glory.
It's whether they see and recognise him now that's important.
When Jesus cast demons out of people, the demons were forbidden from speaking because they knew who Jesus was, Mark 1:34. On one occasion we are told that a demon recognised him, "I know who you are; the Holy One of God", Mark 1:24. Demons recognised Jesus and had to submit to his authority and Lordship - does that mean they were saved?
James says that even demons believe, and tremble. That belief does not save them.