Well the OP has LONG SINCE moved on from this topic, so they aren't even here to correct people, but I know I sure am sick of having to point out to responses here that they're ignoring the topic... Lonesome fucking Road. The same tactics used to clear out Quarry Junction, Deadwind Cavern, the hills outside Vault 19, or even Deathclaw Promontory do not apply to Lonesome Road when you walk into a crevice to loot a suitcase only for a Deathclaw to spawn DIRECTLY on top of you (literally) and is scripted to walk in your exact direction. And this is what half of the Deathclaws do in Lonesome Road. Like the Tunnelers, they're scripted to just appear out of nowhere when you cross a certain spot and to home in on your location. There are approximately 5 Deathclaws on the High Road that are sitting ducks for any sniper, and 2 in the final open area, but the rest are all extremely dangerous and impossible to avoid. As pointed out by another here, earlier, "Lonesome Road cheats".
"riot shotgun with stay back does wonders" is about the best advice that transcends the rest, but even then you're at the mercy of RNG. I've spent entire clips of a Riot Shotgun (in the tame Quarry Junction, no less) without downing a Deathclaw, despite my happy success with And Stay Back!, so this still isn't a guarantee.