For fear of sounding snarky, the best thing to do is to go to the source to check the life expectancy of your LED light bulbs. Each make and model is unique. There's no sense guessing.
Most LED light bulbs have manufacturer's identification on them somewhere. They are either a bar label, OEM, or some similar identification label. Get that off the light bulb, then check the specs online. From there, you should have all the details you’ll need.
At this point, hopefully, there's a receipt somewhere that suggests when the light bulb was installed. Even better, there's a record in an email or a project management system.
If none of these are helpful (or exist), then hopefully someone somewhere has a record of when the signage was installed. Start there. And, if you don't have that, ask your signage company. If you don't have that, then just assume today. It's better to assume the worst than to risk going through your peak season with the chance that you won't be able to properly get your message out.
Your LED light bulbs, like other business assets, are investments. Trying to find the bargain-basement priced knock-offs or alternatives typically give you bargain-basement results. In some cases, they'll void your signage's warranty. Avoid them as if they were the plague.
That calendar / project management system we were talking about? There's no better time than the present to include signage maintenance in your calendar. Double-bonus point score for calendar software that has recurring reminders. If you're looking for a free one, check out Google Calendar or Asana.
With a little luck, going through the process above will put you in a position to never again worry about what to do next for your LED outdoor sign.