"I will acquiesce to your request expeditiously."
No, that's a bit too 1800's. Something more modern.
"Let me take a look."
No, too passive. No commitment to action.
"I'm on it."
Brief, action oriented. Could be a winner, but it's still missing a bit of creative flair.
Hmmm....
"Lauren's on it"
Ding, ding, ding. Winner!
It maintains the brevity of the previous idea, but combines it...