Yes indeed.
The lake of fire is in the context of the new Jerusalem.
In terms of the forthcoming destruction on Jerusalem of old, yes — there was a 40yr transitional period AD30—70 where the two existed side-by-side (Mt 13:30) but in the end-of-the-age the old was fully done away… seen literally in the lake of fire — the very thing Jerusalem and in particular the Temple became as it was razed in a blaze, molten of flames; like the Cross it is literal history which wrought great spiritual significance.
Nowhere does the Bible say the lake of fire is Gehenna.
Not in so many literal words BUT certainly in the words pictures of Jesus’ “gehenna” — I agree with Paidion that gehenna and the lake of fire are one and the same (albeit Paidion views its application as different, though both entities as one and the same nonetheless).
There’s and earthly Jerusalem and a new Jerusalem.
These were emblematic of the co-exiting respective covenants of that era, old and new, as per Paul…
Gal 4:24-26 …which things are symbolic. For these are the two covenants: the one from Mount Sinai which gives birth to bondage, which is Hagar— for this Hagar is Mount Sinai in Arabia, and corresponds to the Jerusalem which now is, and is in bondage with her children— but the Jerusalem above is free, which is the mother of us all.