Yes, the scent must now be in your hand before Lola gets the treats. HOWEVER, you can praise her and start the party WHILE you are gathering up the scent. Yet another opportunity to build duration You will be working with both hands to put the truffle away so rewarding from either hand is fine. Try to keep it close to the scent for good measure.
The time that you are taking to gather up the “truffle” still needs to be exciting. If you watch the demo video of Da Vinci, you can see him practically vibrating as I put the truffle away and get out his hot dog/ cheese/ etc. He will often come close to knocking me down. Start the party with the alert but pay up after the truffle is in hand.
2″ was too deep. Scent changes a bit when it is in the ground. Start by nesting it in the earth so it is still partially visible. Then move to LIGHTLY covering it. Then just barely out of sight (you may spend a little more time at this stage). Then very gradually bury it deeper and deeper. Make sure you always mix in some easy ones too. I will still bury some and leave other out on top of the ground or nested in grass.
Trust your dog! There is no reason to question the alerts. Since you are holding onto the treats until the truffle is in hand, there won’t be any harm in trusting her and acting on it. Go look where she is alerting. If there isn’t a truffle there, simply give her cue again and carry on. Lola need to know that if she alerts, you will look…every time