Thats inside.It needs a mop out. The bricks are a pale yellow rated to 1300c normally used for kilns,furnaces etc.
I have a 2 x temp probe at the left & right of top of arch 2 hooked up to a metre.
I struggle with level ,the fire brick skin came out really well & you can pick up slack by shaping the bricks in the arch but the external skin wandered which lead to lots of cursing by carpenter when we did the roof structure & comments like "How drunk were you when you laid these bricks? " Is this some leaning tower of Pizza .Was there some localised earth quake in this street ?"etc.Every one is a comedienne
I love the idea of lava rock ,dome may be a bit of a challenge to get it to close & neck in. I figure as a boat builder you can bend some thin timber to act as a support while the mortar sets then just burn it out .You can probably shape a keystone to fit the top of the dome & exert the requisite pressure like the keystone in a Roman arch or those pre fab kit ovens made out of terracotta.
Anyway I will wait until you start or ask me a question which ever comes first.
One thought I had Mick for making the dome is to compact wet sand form the shape and then build the dome Scoop out the sand when you are done. This is a popular method used when making a cob oven. The natural lava rock here can be found in brick like chunks that have some consistency in shape and size. They stack quite nicely. I does take sometime though to aquire said rocks. If I still lived out of town wouldn't be a problem, had 5 acres of great rocks!