I have had no issues with Hornady's #H43 shell holder. They are available at Academy usually. I have two of them and they work well. It holds well enough to use my bullet puller which takes a ton of force.
I am not surprised that your buddy is having issues with the Lee shell holder for .338 Lapua. I bought one of their case trimmer setups and it doesn't hold the cases worth a crap. I have to center the case perfectly for it to hold the case and one hair off and the case pops out. I contacted them about it and they sent me a new one. The new one is only marginally better.
I am at the point of drilling and tapping a Hornady shell holder to use in the Lee trimmer.
I think just get anything but a Lee and your buddy will be fine.