Should PFCs stand at "Parade Rest" for a SPC?

Absolutely not. LTs should not be saluting one another and Specialist has not authority to be putting an E3 at parade rest. That's just someone being power hungry. That's just someone who needs a good ass chewing.

SPC is still a automatic rank that anyone can achieve just by being able to breath. Nobody should be standing at parade rest for a SPC.

Many people have difficulty when given authority, whether it be authorized or wrongly perceived. Sometimes a friendly chat can help solve this, sometimes a swift kick in the ass, or, at the worst, some wall-to-wall counselling in the First Sergeant's office (yep, that one dates me).

In a lot of units, officers and NCO's can be pretty scarce at times so inexperienced SPC's tend to get away with this kind of thing because the officers and NCO's are off doing their other duties and no one is watching. From my experience in an aviation unit where you have 4 Commissioned Officers and 26 Warrant Officers hanging around, we were able to nip this in the bud with some friendly chats (plus being 6'5" and 230 lbs helped a little)

And we were also able to talk to the PFC's and SPC's when they were acting up with a new promoted NCO. It was all about finding the proper way to motivate someone to learn and asking, "How would you want to be treated?"

This is why Marines don't have "Specialist"

Maybe the 2 LT's were married and he salutes her at home, too?

A SPC is not an NCO, therefore no, a PFC should not be required to stand at Parade Rest for a SPC, however the PFC should stand at Parade Rest for a CPL. If a PFC chooses out of respect for the SPC's rank, then that's their own choice.

If the 1SG wants it to happen, then so be it! NCOs better make it equal in each PLT and enforce the good training! To easy!!

I think that all E4 Specialists and below belong to the SPEC4 Mafia and therefore don't stand at parade rest for each other.

The vast majority of lieutenants do not salute each other in the Army. I have never seen or heard of anyone under the rank of E5 being required to give any courtesy to a fellow pvt-spc. For example at basic training despite the fact that there's a gang of specialist trainies running around, everyone is referred to as private. The same ideas apply to the regular Army and individuals under E5 don't have any courtesies to extend to their superiors who are themselves under E5. However even in basic training I've seen e fives that needed to go through training again and they were required to enforce courtesies for themselves. The drill sergeants were mad when sergeants E5 in training, even basic training, weren't given courtesies by the trainees ranked E four and below.

Good luck.

Noth Specialist and Corporal are junior NCO'S the only difference is leadership positions vs technical not much different than the WO and Officer relationship. When in doubt look it up.