Moving E6430 Win 7 Hard Drive to another identical laptop. Problems?

You'll want to make sure that whatever replacement you purchase is licensed for the same version of Windows you're currently running, including the edition (Home Premium, Pro, etc).  OEM licenses are explicitly NOT transferable to other systems the way licenses purchased at retail (separate from a PC) are, and when you move your drive to another PC, there's a decent chance Windows will detect that several components have changed (based on MAC address, motherboard unique ID, etc) and fall out of activation. If that happens, you'll need to supply a different product key, hence the need for your new system to have its own, which should then activate despite the fact that you've got a different hard drive installed.

If you upgraded from an OEM Windows 7 license to Windows 10, then once again you'll want to make sure that the license on the PC you're buying also had ITS license upgraded to Windows 10, otherwise you'll have the same problem I mentioned above -- and Microsoft isn't allowing free upgrades to Win10 anymore, so just having a Windows 7 license on the new PC won't be enough to reactivate your Win10 installation if that's what you have.

In terms of swapping models, a change that small shouldn't be a problem -- worst case you may need to install a few different drivers, e.g. the video card.  However, I'm not sure about this.  It's certainly the case that just dropping a hard drive from one system into another without doing any prep work can make that drive unbootable on the new system because certain critical drivers won't be correct for the new system.  In that case, there are some backup and recovery applications that specifically deal with handling this type of migration. Macrium Reflect is one, and the feature that handles this is Macrium ReDeploy, though it's only included with their paid versions.  Note that you wouldn't technically even have to do a backup and restore to use ReDeploy.  If you transplanted the drive, you could simply boot from your Reflect Rescue Media and then immediately run ReDeploy to adjust the configuration of the drive for the new system's hardware.