No distributed system is guaranteed to make forward progress if over 1/3 of its voting nodes is faulty, full stop. Once an adaptive adversary controls more than 1/3 of the voting power, they can forever delay the remaining 2/3 of the voting nodes from reaching consensus. Hell, they'd even be able to delay votes from other nodes to slash their stolen stash.

From this, I can conclude at least one of the following:

* LMD GHOST is incorrect

* your understanding of it is incorrect

* LMD GHOST is not a BFT consensus algorithm