why should I spray something on my lawn????
Because YOU would also be willing to take the much longer, more difficult, more labor-intensive, and more expensive path of the live trap. Since you don’t know the owner, only YOU can do anything anyway. Where is the logic in choosing the most complicated of a few possible solutions?
Unless, of course, you don’t actually want the most effective problem solution but see yourself as having an educational mission toward the owners. Whom, of course, you will only find if you first keep the cat for so long until the owners post search notices.
How much do a live trap and keeping the caught cat cost, in money and time? But with a cheap solution for a few euros and a time investment of seconds, you ask why YOU should bother so much? Seriously?