Active player has Omnath, Locus of Mana enchanted with Lust for War and 2 green mana (floating) in his mana pool. Non active player controls Ghostly Prison. Can the active player choose not to attack with Omnath? Why?

Yes, they can choose not to attack. Due to the last line of 508.1d, they are not required to pay the cost to enable the creature to attack. Having the mana in their mana pool doesn't matter, they are not required to pay the cost if they don't want to, and will not be forced to attack with Omnath.

508.1d The active player checks each creature he or she controls to see whether it’s affected by any requirements (effects that say a creature must attack, or that it must attack if some condition is met). If the number of requirements that are being obeyed is fewer than the maximum possible number of requirements that could be obeyed without disobeying any restrictions, the declaration of attackers is illegal. If a creature can’t attack unless a player pays a cost, that player is not required to pay that cost, even if attacking with that creature would increase the number of requirements being obeyed.

Nathan Long
Magic Rules NetRep