Can I reconquer a battlefield I already lost and get its conquer affect in the turn if I already scored?

No, you cannot.

According to Rule 465, a player may only score a battlefield once per turn, regardless of the method used (Hold or Conquer).

As clarified in multiple RiftJudge FAQs (such as FAQ #3484, #6578, and #9691), once you have already scored a battlefield during your turn—whether by holding it at the start of your turn or by conquering it earlier—you have reached the scoring limit for that location for the remainder of the turn.

Because conquering is inherently tied to the act of scoring a battlefield (Rule 464.1), you cannot trigger conquest effects if you are unable to score the battlefield. Moving your units away and returning to regain control later in the same turn does not reset this restriction, and therefore will not allow you to trigger its conquer effects again.