Can I use 340 (LA) camshaft, lifters, & timing chain in a 360 Magnum?

All those parts will fit no problem, I've done it before myself. You might not even need custom-length pushrods since you're using LA heads; there is a slight difference in deck height between Magnums and LAs but that's the only factor I could think of which would influence pushrod length and we're talking maybe .010" or less? If the plan is to swap the Magnum into a classic you'll want the LA-style timing cover anyway, Magnum timing cover puts the accessories kinda high up and looks weird in an old car IMO.

I'd only be concerned about the EFI, roller lifters etc. if I was putting it in a 90s-2000s truck like they came out of.

Engine in my Duster is a 2000 5.9L block+crank+rods+pistons, Edelbrock LA heads and non-Air Gap RPM intake, custom-grind hyd roller cam with long snout for fuel pump drive, reused stock Magnum lifters, LA timing cover, LA double-roller timing set, LA headers, PRW damper with Magnum offset weight, reused Magnum flex plate. Sounds like Frankenstein but it pretty much all just bolted together like any old small block.