I disagree. The strongpoint of lawful evil and it's ability to remain party-friendly is in the fact that nothing they do is technically illegal. A lawful evil individual is much akin to a politician, they'll use the system to protect themselves, enrich themselves and generally screw everyone else over.
To the first part, they may not, but neutral and lawful evil shouldn't view them as necessary either. Neutral evil tortures because it is efficient.
Like true neutral, their concern is a resolution, they just have a lower moral code. A lawful evil person with torture because it is legal (or the law is looking away) and because it is efficient. Chaotic evil tortures for pleasure and fun, regardless of if it is the best way to resolve a situation.
I don't disagree with the last part, but for neutral and lawful evil, the situation ought to warrant it. If the success of Mr Lawful Evil's plans requires the death of everyone they hold dear, yes they will kill them all. By the same token, it doesn't mean they revel in the bloodshed. They may slit their throats in the night or use fast-acting poisons. Again, the concern is selfish and expedient. They're not killing these people because killing is fun, they're killing them because greater goals (namely: their own) are at stake.
I think there's a general misconception that evil means murder. I don't think that's accurate or fair. That's really what my point is and why I see neutral evil and lawful evil as party-friendly.