Lava Monsters are the first Mobs added in the Lava Biome, the being second one the Lava Dragon. Lava Monsters drop Flames, which are used in the Protection Gears, as well as Reidite Arrows. When come in contact with the player, they take away half of your current ice cubes (capped at 250), which can cause you to die of heat unless you go back to the winter and get more.
The best way to kill this is to kite it toward the border between the sea and lava biome, and stand in the sea. To do this, you should use bridges or a diving mask. Since you move faster than lava monsters, you will need to hold attack as you lead them. Since you usually need several flames, try to stack multiple lava monsters at once.
You can also kill a lava monster the same way you would kill an arctic fox (by attacking slowly). However, you are more likely to get hit if you use this method, meaning that you are more likely to run out of ice.
The lava monster was added in the "It Smells Like Burning!" update. Originally, lava monsters were 80% resistant to most weapons, except reidite and lava. As of an unknown update, you can kill lava monsters with any weapon, although this change is not shown in the changelog, and the tooltips of reidite weapons are still "Really useful against lava monsters".