Star spring Battlefied: I conquer it with a sprite, I score the point, can I play Lillia on the battlefied, target Lillia herself to be sent to base and play another sprite on the battlefield due movement trigger for a total of 2 sprite at the Star Spring? Is a legal move?

No — that line isn't legal. Star Spring's trigger says "move another unit they control here to its base," and "another" means a unit other than the one whose play triggered the ability — so when you play Lillia, she can't be the one sent back. The only eligible unit at the battlefield would be the conquering Sprite itself (tokens don't even trigger Star Spring, per FAQ #10351 — only non-token plays do).

If you moved that Sprite to base instead, no second Sprite appears, because Lillia never moved and her trigger requires her to move (Rule 449 — abilities can cause a Move, and Lillia's trigger would fire on it, but only if she's the one moved). So you can't end with 2 Sprites at Star Spring through this sequence. You'd need a separate effect that moves Lillia herself to base to get the second Sprite.