I'm sorry if someone has already asked this question but I have been trying to find this information in several different places and have no idea how to word what I'm asking. The example I mean is this: if I cast Lure on a creature and attack while I also have a Heat Wave in play, does my opponent have to pay the life, or are they considered "not able"?
If a creature can't attack or block unless a cost is paid (whether it involves paying life or not), then the active player "is not required to pay that cost, even if [attacking or blocking] with that creature would increase the number of requirements being obeyed" (C.R. 508.1d, 509.1c). If the cost is not paid, the creature is simply not "able" to attack or block.
EDIT: Generalize to blocking after comment 3 was posted.
Blocks that would require more life than they have are illegal, because that life payment is not met, because it is not legal to pay life you don't have.
Blocks that do not include some creatures, on the creature with Lure, are valid even given the combat requirements expressed through "if able" on Lure's text, because Heat Wave imposes a restriction with a cost to escape it, and CR509.1c says to allow exactly this.
Your opponent can block with anything in between these extremes - no creatures, some, or all anyway, unless they would pay more life than they have. They may even block and pay all of their life, if they have that many creatures, and wanted to pay all their life for some reason.
All while Blue creatures cannot block here, of course.
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EDIT: Generalize to blocking after comment 3 was posted.
Blocks that do not include some creatures, on the creature with Lure, are valid even given the combat requirements expressed through "if able" on Lure's text, because Heat Wave imposes a restriction with a cost to escape it, and CR509.1c says to allow exactly this.
Your opponent can block with anything in between these extremes - no creatures, some, or all anyway, unless they would pay more life than they have. They may even block and pay all of their life, if they have that many creatures, and wanted to pay all their life for some reason.
All while Blue creatures cannot block here, of course.
Awesome avatar provided by Krashbot @ [Epic Graphics].