Once a player has announced that they are casting The Lord of the Eagles, no player may take actions to try and change the power of creatures its controller controls before that spell's cost is locked in.

The total cost to cast The Lord of the Eagles is locked in before you pay that cost. For example, if you control three flying creatures, each with power 2, including one you can sacrifice to add {C}, the total cost of The Lord of the Eagles is {1}{U}{U}. Then you can sacrifice the creature as you activate mana abilities just before paying the cost.

The cost reduction ability reduces only the generic mana in the cost to cast The Lord of the Eagles. The colored mana must still be paid.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of The Lord of the Eagles). The mana value of the spell remains unchanged, no matter what the total cost to cast it was.