This is an off-the-wall question, but I was wondering something: Could the Lake of Fire be the "Baptism by fire" mentioned in Matthew 3:11? Or is there no way the two could be one and the same thing?
Yes.
Matthew 3 and Luke 3 speak of both the Baptism of the holy spirit and the baptism of fire. Both also deal with the then coming Judgment. "The axe is already laid to the root of the trees"
This is the same as the lake of fire. The catastrophic end of the old covenant system.
Mark 1 and John 1 both speak of the baptism of the Holy Spirit but not of the Baptism of fire. And of course then neither one is addressing "judgment" either. This is the consistency of the 4 gospels.
When addressing the baptism of fire, in kind then, the Judgment, the wrath to come or "wrath about to be" was also addressed.
When only the baptism of the Holy Spirit is mentioned then we do not also in kind, see the "who warned you to flee from the wrath to come?" and "the axe is already laid to the root of the trees".
"And do not say within yourselves that you have Abraham as your father, for God is from these stones able...."
This is what they were told to repent from. The dead works of the old system.
Barry