Can I merge two Apple IDs for data recovery?

Until and unless access to the lost Apple Account is regained, there is nothing to merge.

How to use account recovery when you can’t reset your Apple Account password - Apple Support

As for the Apple Watch, Activation Lock is intended as a theft deterrent, and means providing the associated Apple Account and password to unlock it, or providing an original purchase receipt to Apple to release the lock.

Elizabeth Rodriguez wrote:

Thanks for your answer and link.

My friend just found her Apple ID password for the original account that was lost. Is there a possibility to correct the issues?

Usual would be to switch back to the original Apple Account, and discard the new and its contents.

This if there’s not been a great deal of info stored locally in the new account. This is the simplest.

If there is new data to be preserved and merged, the following sequence would be used to get the data all onto the local iPhone (assuming there’s enough storage), and then switching to the original account:

How to “unshare” an Apple ID - Apple Community

To be very clear, you do not need to create a new Apple Account (as described in that linked sequence), ypu will be merging to the original.

Purchases and subscriptions cannot be migrated. (Yes, Apple does now have a procedure for that purchase-related merge, but that procedure probably isn’t all that applicable here, given what you’re requesting. You want to move your data, and that’s what the ”unshare” procedure does.)

Migrate purchases from one Apple Account to another Apple Account - Apple Support