There are some verses in his gospel that no witness could have related to Luke.
I don’t know what makes you think that.
Like what the angel said to Zechariah (Luke 1:12 et seq.), who was surely deceased before Luke ever got the notion to write his gospel.
And so was everyone else who heard what Zechariah said?
Like what the angels said to the shepherds at Christ's birth (Luke 2:10-12).
How do you know that all of them were dead? Jesus was born c. 4 B.C.
Luke’s second book (Acts) can be dated to approximately 62 A.D. -> Luke wrote his first book sometime before 62 A.D. but how long before is debatable.
For the sake of discussion, let’s put his Gospel at 62 A.D. -> 4 B.C. + 62 A.D. = 66 years.
How old were the shepherd’s in the field? The job was often performed by teenagers. Let’s say that there was a 13 year old shepherd among them. 66 + 13 = 79 years old. Let’s round it up to 80. Are you certain that there were no 80 year old men living at the time whom Luke could have interviewed before he wrote his Gospel?
Like what the Devil said to Jesus in the wilderness (Luke 4:1-12).
When did the (alleged?) conversation between Jesus and the devil take place? Let’s place it at approximately 30 A.D. -> approximately 32 years before Luke wrote his Gospel.
Are you certain that Jesus didn’t tell anyone at all what the devil said to him in the wilderness?
Let’s say that Jesus told someone his own age about the conversation. A 34 year old would have been 62 years old when Luke later investigated and wrote his Gospel around 62 A.D. Are you certain that there was no 68 year old person living who could tell Luke what Jesus had told him?
Tradition tells us that Luke interviewed Mary. Mary would have been around 13 years old when she gave birth to Jesus. If we date the death of Jesus to approximately 33 A.D -> Mary would have been approximately 46 years old at the time of his death. Did Jesus tell Mary what was said in his conversation with the devil? Are you certain that he didn’t?
How old would Mary have been in 62 A.D.? —> 46 + 29 = 75 years old. Are you certain that it isn’t possible that Luke could have spoken with the 75 year old mother of Jesus?
Luke fabricated the stories? There are no witnesses who could have related these examples hou offered flr our consideration to him?
“Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. Therefore, since I myself have carefully investigated everything from the beginning, it seemed good to me write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught.”
(Luke 1:1-4, NIV)
Luke says that there were, and Luke didn’t write in a vacuum. No biblical writer says about Luke what you’ve said about him.