Lava isn't a defined type, but it's obviously very damaging to objects.
The default stats for a one handed blade are 10 hardness (derived from being steel) and 5 hit points (derived from being 1/6th an inch of steel).
An adamantine longsword will have 15 hardness and 7 hit points.
The sword took 7 points of lava damage. The question then is, how good is lava? My assumption at the time was that it completely ignored hardness, but that seems really unlikely to be correct.
Instead, we'll have lava quarter hardness, which is the 3.X value for really object-damaging energy types, such as sonic. This means that stabbing it with an adamantine object will be three less than the value rolled, and striking with an iron object would mean iron's hardness subtracts 2 from the damage dealt.
So presumably Ichabod's sword is at 4 hit points, not 1.
This also means that the sword does not have the broken (
https://www.d20pfsrd.com/gamemastering/ ... TOC-Broken ) condition yet. The reflective damage to the object and the melee attacker is 1d6, so a roll of 4 or better would give it the broken state (by dealing 1 point of damage, taking it to less than half), with a max roll reducing it to 1 hit point.
Note that objects that have the broken condition can still be repaired, either mundanely or with trivial magic, such as mending (
https://www.d20pfsrd.com/magic/all-spells/m/mending/ ), which restores 1d4 hit points per cast and can be spammed once per round when out of combat, assuming anyone knows it as a cantrip or orison.