La before a verb
 

Hi,

Y en mi ciudad natal había unos tíos que la tomaban siempre conmigo.

And there were these fellows in my home town who used to take after me pretty regularly.

Lexicalized pronoun again? If so, what would be its "infinitive" and definition?

UPD

Another usage:

Yo no era el único con quien la tomaba.

I don't quite understand what "take after me" means there. I only know it as "to resemble someone or to follow someone's example", but the context suggests something like "to pick at or bull someone". If that's the case it would be "la tomaban conmigo" (verb: tomarla, with lexicalized pronoun) meaning "they have it in for me".

The use varies regionally. I'd use "se la agarraban conmigo" (agarrárselas)

Probably the same use, although I'm not familiar with that use.

I would use "tomar/agarrar/tener de punto (a alguien)", but it's regional.

Something like that, yes. Thanks!

I thought the la referred to a beer or some other beverage with a the female gender.

The phrase is tomarla con alguien. As Alec points out, it means 'to have it in for somebody.'
The English translation given in the original post is incorrect.