Leyline Tyrant's last ability goes on the stack without a target. While that ability is resolving, you may pay any amount of red mana, including from the unspent mana you have. If you do, a second ability triggers and you pick one target to be dealt that much damage. This is different from abilities that say "If you do . . ." in that players may cast spells and activate abilities after mana is paid but before the damage is dealt.