The 1906 LDS large-print edition accidentally changed the determiner that to the, but this error was restricted to this single edition. The use of that to refer to the “lake of fire and brimstone” is perfectly acceptable since it was just referred to in verse 16 (“their torment is a lake of fire and brimstone”). Similarly, the that of “that awful monster” (also here in verse 19) is appropriate since earlier (in verse 10) death and hell was referred to as an awful monster.
Summary: Maintain in 2 Nephi 9:19 the use of the determiner that (“that lake of fire and brimstone”).