Is this grammatical construction an imperative for the third person?

"Let" can introduce an imperative phrase, but it doesn't have to. Third person is a red herring here; "Let us go forth in peace" at the end of Anglican communions has exactly the same force of command. Exactly how strong an imperative it is depends very much on the context, though. It's not terribly strong in either your example or mine, but "Let my people go!" is a different kettle of fish entirely.

If I recall correctly, "Let + verb" is the standard way of translating subjunctive "imperatives" from Latin.

"Let" can be used in the imperative mood for the following purposes:

A command insisting someone allow something to happen

Let him go!

A polite way of making or responding to a suggestion

Shall we go? ... Yes, let's.

A polite way of offering help

Here, let me.

Expressing a strong desire for something to happen or be the case

Let him be all right.

Expressing defiance or a challenge

If he wants to walk out, well, let him!

Expressing an assumption upon which a theory or calculation is based

Let A and B stand for X and Y, respectively

These are all in imperatives, though only the first would actually be an order/command (and maybe the fifth). The fourth would be the one you're looking for, and it is in the imperative mood (though not necessarily an order/command).

Source: New Oxford American Dictionary

I read it as an exhortation rather than as an order. But I don't know the jussive subjunctive, so let us now go look that up...