Here are the relevant phrases in support of my answer, from the rules for Opportunity Attacks.
You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack occurs right before the creature leaves your reach.
You can avoid provoking an opportunity attack by taking the Disengage action. You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction.
1) Lightning Lure does not result in the target moving of their own volition. It moves them without using their movement, action or reaction, and a standard Opportunity Attack only occurs if a target moves of their own volition (or while under the effect of some charm or other condition that causes them to move by coercion as if they had done so willingly).
2) Polearm Master only explicitly extends the general rule that Opportunity Attacks happen when you leave a creature's reach with a specific extension that it can happen when you enter a creature's reach. The contrast of the words "leave" and "enter" implies that Polearm Master is only intended to alter the direction of intentional movement on the part of the target that triggers the Opportunity Attack, not other aspects of how Opportunity Attacks work. If that were not so, we would expect the Polearm Master description to state a special exception to the general rule by allowing this Opportunity Attack to trigger against a target that is unwillingly moved, but in the absence of such an exception the prohibition on unwilling movement in point 1 still applies.