Does the lawyer get the deposit 'in trust' until the deal closes?
Yes, but you give the deposit to a notary. But not all will take it, it's not mandatory by law yet. You need to ask about the possibility.
The Notaries Law, which regulates the most important issues related to the activities of notaries, recognizes that the acceptance of deposits is one of the notarial activities. However, the regulations do not require notary accepting deposits, and only allow such action. So if the property seller wishes to carry out the transaction in this way, he needs to find a notary office, which will agree to.
Notary puts the money on a special bank account. It's good to pay it before the notarial deed, to meet the transfer deadline. Seller gets the money at the time of land registration. Otherwise, the notary is obliged to hand over the amount due.