grammatical number - Should a noun following "singular they" be singular or plural?

I've understood how to use singular they on a single sentence, but the problem comes with articulated sentences like this one:

If a person lies to you this way, they are probably thieves.

My doubt is about its correctness, I would also say it this way:

If a person lies to you this way, they are probably a thief.

Is the second sentence correct?

Answer

Try:

If {a person / someone} lies to you like this, they are probably a thief. [Singular subject]

If people lie to you like this, they're probably thieves. [Plural subject]