If a player plays Lecturing Yordle on a battlefield they control, opponent reacts with Gust to send it back to hand, does the player still draw a card?

Yes, the player still draws a card.

According to the rules and established game mechanics (as seen in similar interactions like the Traveling Merchant FAQ), when a unit is played, its "When you play me" ability triggers and is placed on the chain. Because the ability has already triggered and been added to the chain, it will resolve regardless of whether the unit is subsequently removed from the battlefield by a reaction like Gust.

Sequence:

1. The player plays Lecturing Yordle.
2. The "When you play me, draw 1" ability triggers and is placed on the chain.
3. The opponent reacts with Gust, targeting the Lecturing Yordle.
4. Gust resolves first (as it is the most recent item on the chain), returning the Lecturing Yordle to the owner's hand.
5. The "draw 1" ability then resolves, and the player draws a card.