I have Lucian with Warmog's on him, I conquer Sunken Temple. Can I spend 1 to draw as he is now mighty?

No, you cannot use the effect of Sunken Temple to draw a card in this scenario.

Here is the breakdown of why:

1. Mighty Definition: According to Rule 708, a unit is "Mighty" only if its Might is 5 or greater.
2. Trigger Timing: Sunken Temple's ability is a triggered ability that checks for a Mighty unit at the exact moment you conquer. If the unit does not have 5 or more Might at the moment the conquer occurs, the trigger condition is not met.

Even if you were to receive a buff from another source after the conquer, it would be too late to satisfy the condition for Sunken Temple. The unit must be Mighty at the exact moment the conquer happens for the ability to trigger.

Note: I could not fully verify this ruling against the retrieved rules.