My son lost his iPhone in a lake... Ugh !

Even if you did have Applecare + you would not be able to use it. With the warranty you need to bring the damaged phone in for replacement. As the phone is lost in the lake you don't have that.

You would need to check with your insurance provider if your covered or pay full retail for a new phone if you are not due for an upgrade.

There is the AppleCare+ plan that covers it (in exchange for a 49$ fee) but you have to have subscribed to it before.

Use Find My iPhone! Then maybe you can scuba down to retrieve it. 😝

The terms for AppleCare+ explicitly do NOT cover loss or theft. You have to have the covered device in hand to turn in for the accidental damage claim.