How do I update Lightroom metadata after using ExifTool without wiping my edits?

I would ask this as a comment but I don't have enough reputation (yet) so I'm starting with my comment/question, then will give an answer.

Are your photos in RAW or jpeg or other format?

If your photos are in RAW, (the use case I'm most familiar with), LR has the option to store the develop information in sidecar .xmp files. See this tutorial:

http://blogs.adobe.com/jkost/2011/08/lr3-saving-changes-metadata-to-files-in-lightroom.html

After saving the metadata (LR edit changes) to .xmp move the RAW files to a different folder, and import them again into a new catalog with the new date metadata (stored in the RAW file and edited with exiftool). Then after the photos are in LR with the correct date, move the .xmp files into the same folder, and then update the files with the "new" metadata. This should bring back all your LR edits while retaining the changed date.

Test it first!

Make 2 new folders. Copy a few RAW files to one folder, and copy their companion .xmp files to the other folder. Make a new catalog, import the RAW files and make sure the date is now correct. Move the .xmp files into the folder with the RAW and then tell LR to update the metadata and see if it works. If it does, you can delete these copies (you made copies, right?) and catalog, and do it all again with all the files.

I'm assuming you have many other photos in LR but for this process I'd make a new catalog just for these photos, and make sure everything is as you want it, then "import from catalog" to bring them into your main catalog.

You are probably changing the metadata with exiftool before changes are written by Lightroom. To ensure you don't loose LR changes when using exiftool; Make the develop changes in Lightrooom, save metadata in LR, run exiftool, then read metadata in LR.

If this issue is still live, and you have some skills in programming, the Adobe scripting language (https://www.adobe.com/content/dam/Adobe/en/devnet/scripting/pdfs/javascript_tools_guide.pdf) has the capability to read/edit metadata. (10 Scripting Access to XMP Metadata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page. 257)

Lightroom has an "Edit Capture Time" feature built-in: While in Grid mode, go to Metadata | Edit Capture Time. One of the option is to Shift by a set number of (full) hours.

Nik Gaffney is correct re: how to handle integrating ExifTool edits. I do this all the time (for different reasons).

But...

You can do your adjustment from in Lightroom.

The "Adjust to a specified date and time" option to "Edit Capture Time..." doesn't work with multi-item selections the way the interface implies it does. It looks like it changes everything to the same time, right? But that'd be silly.

What it actually does is exactly what you want: Pick a time 3.5 hours later for the current image and everything will get shifted 3.5 hours.