Have face it... but since I know her well so it will not an issues
No, you should not issue to the lawyer's own name (Vendor). Some alternatives I can suggest:-
1. Ask the Vendor who is also a lawyer to prepare the SPA asap and deposit 10% to lock Purchaser & Vendor in.
2. Write a letter of intent to purchase the property and the cheque beneficiary should be in the Law Firm's name as stakeholder. Google "Letter of Intent Real Estate" and sample templates are available. In the event the SPA cannot be perfected, all monies should be refunded.
You should also consult your own lawyer or legal friend because you are facing a lawyer. Some of the time, the SPA will be drafted against your favour, which is not in line with normal industry standard.