Grammaticality of "Don't let's get you cheap"

I have come across a sentence in one of my textbooks with which I seem to have some problems. One just needs to translate it, paying attention to the verb "hold" used with the appropriate particles. Here it is:

"That's right, Bill. Hold out against it. Put out your strength. Don't let's get you cheap".

The part of it, marked in bold, quite baffles me. I have stumbled upon a number of misprints in this textbook, so it may well be one of them here, too, but it appears to be a line from the George Bernard Shaw play Major Barbara (1905).

Let us

"Let's" is a contraction of "Let us". Expand that, and the sentence is pretty straightforward.

• Don't let us get you cheap

The meaning here is the literal meaning, but to understand it, you have to see the line in context. The character who says this, Barbara, is trying to get the other character, Bill, to mend his ways and join the Salvation Army.

to not win cheaply

In the quote your sentence comes from, she's goading him, telling him to resist her message as strongly as he can, so that they do not "get" (i.e., convert) him without significant cost.

BARBARA. You're not getting converted, are you?

BILL [with conviction] Not ME. Not likely. Not arf.

BARBARA. That's right, Bill. Hold out against it. Put out your strength. Don't let's get you cheap. ...

"But people don't never speak proper anyhow..."

Finally, grammatically speaking, "cheap" should be "cheaply", as it's an adverb for "to get".

However, Shaw is representing speech, and speech is much more fluid when it comes to grammar. This particular use of adjectives for adverbs is common even today in South-Eastern England, to the point that when I read that line, I immediately imagined a woman from the East End of London saying it.