How old is your battery?

12.6V is a fully charged battery and it should only drop about 2V from your open circit reading when cranking.
You are starting at 12.4 and dropping to 10v when cranking...battery is dead.
You can confirm this with a load test but I will bet my good battery on it!!
Your lights on test is a good indicator of load, it should maintain above 12V with lights on and the fact its not...battery has no capacity.
Once you get this sorted you will need to throw the DMM (meter) onit while the engine is running to ensure that the charging circuit is ok. It could be the reason your battery is dead. While running the output voltage syhould be between 13.5-14.5V and not go over 14.5V when revving it.

Matt.