if lecturing yordle conquors and leblanc make a reflection token of it does that reflection draw as well?

No — the Reflection token does not draw.

"When you play me, draw 1" is a play effect (Rule 383.4.a), and it only fires when the permanent carrying that ability is played to the board. The Reflection token is played as a 0 [M] token; the copy effect that turns it into Lecturing Yordle only applies after it has entered and resolved (see the Zilean/Deceiver timing FAQ). Since the token was never "played" as Lecturing Yordle, its copied play effect's condition is never met.

The original Lecturing Yordle already drew its card when you played it — conquering with it doesn't re-trigger it, and the copy doesn't grant a second draw.