Lindsay Lohan -- The Pre-Court Starbucks Run

10/22/2010 9:45 AM PDT
With her eyes barely half-open ... a semi-awake Lindsay Lohan hit a Starbucks reaaally early this morning -- for a quick pick-me-up before court.

We're told someone from Lindsay's crew ordered a "bunch of espresso drinks" ... but it's unclear if LiLo personally indulged in the sweet relief of caffeine.

Lindsay's due to appear in court at 8:30 AM -- we'll be streaming the whole thing live.