There seems to be no way to copy a pick list so it could be moved from the lite version to the paid version. Importing the form and contents does not move the pick lists attached to the form/file when moving to the paid version.
The best way to copy over your entire database from the lite to the full version including your pick lists is to do a complete backup using SyncDocs. Please see https://www.tapforms.com/support for instructions on using SyncDocs and where to download it.
Alternatively, if you have the list of items on your computer, you could email them to your iPhone. The pick list items should be each on one per line. Then you could copy the values to the clipboard, create a new Pick List in Tap Forms, then tap “Add values…” then paste them into the text area. Then tap Save. Tap Forms will split all the pick list values up into individual items that you can move around easily.