Command to have lava increase creating a flood
Solution 1:
While there is no single command to make this happen, you could use: /fill x1 y1 z1 x2 y2 z2 lava keep. This works the same as a normal fill command, but doesn't destroy any blocks in its path.
If at the end of the game you wanted to get rid of the lava, you could use: /fill x1 y1 z1 x2 y2 z2 air replace lava. This command replaces every lava block in the selected area with air, thus removing the lava from the area.
If you want more information on the fill command, go here