I also highly recommend having a termination policy that explains how you do handle terminations of all kinds and to specify in that policy what you expect from departing employees and how you handle pay for unused or accrued vacation, return of company property and so forth.
You may want to take a longer-term view of the advantages of paying in lieu of notice by using the leverage paying in lieu of notice can provide to you. That is, you may say in your policy that management will consider paying in lieu of notice in certain situations that make sense for the company and if a resigning employee offers two weeks of working notice, agrees to train whoever will be doing the departing employee’s work, and if all company property is returned in good condition and so forth. Also, your reputation as an employer can be damaged with the employees who are not leaving, just yet, if you treat departing employees in what can be perceived as a spiteful fashion. So, think through how you want to handle this potentially negative matter and strategize what will really be the best practice for you and your business. Hope this is helpful.