Why did Brigadier General Erinmore send two Lance Corporals, not junior commissioned officers?

General Erinmore chose him on purpose because of the fact that Blake's brother was in the same regiment who was going to be pushed forward. Blake will be motivated to somehow get to his brother's regiment and deliver message to save them all.

Following are dialogues from tent briefings at beginning of movie.

SERGEANT SANDERS: Lance Corporals Blake and Schofield, Sir.

GENERAL ERINMORE: Which one of you is Blake?

BLAKE: Sir.

ERINMORE: You have a brother, a Lieutenant in the 2nd Devons?

BLAKE: Yes, sir. Joseph Blake. Is he-

ERINMORE: Alive, as far as I know. And with your help I’d like to keep it that way.

Since the communication lines were cut Erinmore wanted someone with map skills.

ERINMORE: Sanders tells me you’re good with maps. That true?

BLAKE: Good enough, Sir.

It was a smart thinking. An unmotivated soldier might desert in middle of a mission due to the risk associated with it.

Update after Greek - Area 51 Proposal's comment: Thanks, but why didn't Gen Erinmore include a junior commissioned officer with Blake?

Also, Blake and Schofield carried written command by General Erinmore which was supposed to be obeyed by Colonel Mackenzie. Delivering it by a private or by a captain would make no difference.

Rahul has given a stellar answer. Other possible reason could be for practical military purposes.

Bona fides is one possible reason. In military radio communications, we had to constantly verify our identities. Also, when meeting partisan troops, we had to present a prearranged/predetermined form of bona fides. This was usually in the form of a signal, or a challenge and response password. Sometimes, the only bona fides was to have someone well known to the individual identify them on sight or by asking them questions only the true person would know. Spies and subterfuge are common in war. The general might not have had time to arrange a form of bona fides. An unknown junior officer may not be believed. Or worse yet, an unknown junior officer may be shot as a spy. A senior officer would be known, believed, and obeyed. But, the risk of sending a senior officer who might be captured and tortured for information was too great.

The reason for not sending a third person is also very practical from a military sense. The more people sent, the slower they must move for stealth’s sake. That is why recon teams are four to eight men and a sniper team is two.