Can I demand my deposit be held by a lawyer instead of the buyer directly?

Yes, and this is a sensible, common protective step to ask for. If a deposit has been agreed to as part of your LOI, there's no rule requiring it to sit informally with either side rather than being placed in trust with a lawyer — having a neutral lawyer hold the funds until agreed conditions are met is a standard way to make sure the money is actually secured rather than remaining subject to whatever the paying party decides to do with it in the meantime.

A genuinely committed party usually has little reason to object, since escrow doesn't cost them the money any sooner than agreed, and it protects both sides equally by making clear who releases the funds and under what conditions, rather than leaving that to an informal understanding. Resistance to this request is worth paying attention to, since it can signal the funds aren't actually as available as represented.

If you want a deposit held this way, the specific release conditions — what triggers payment to you, what triggers a refund — need to be spelled out clearly in the escrow instructions, not left implied. A Treadstone business lawyer can set up the trust arrangement and draft those conditions precisely.