1) "We never did not have a lecture by this lecturer"
This means that the lecturer would always end up giving you lectures at some rigid and constant frequency throughout your experience. Double negative = affirmative in English.
2) "Never we did not have a lecture by this lecturer"
3) We did not have never a lecture by this lecturer"?
4) We did not have a lecture by this lecturer, never"
All of these are ungrammatical.
2) "Never we did not have a lecture by this lecturer"
There is the antiquated "Never did (subject) (verb)", however. I don't advise using it casually.
3) We did not have never a lecture by this lecturer"?
"Never" never goes after its target verb, unless in some nonstandard speech. It goes before it. e.g. "He was never permitted to enter this facility!"
4) We did not have a lecture by this lecturer, never
Nonstandard.
I'm more familiar with
We did not have a lecture by this lecturer, ever.
though I do not recommend this in formal writing, ever.
Even better would be
We did not ever have a lecture by this lecturer.
EDIT: As it seems that your lecturer did not give you any lectures, just never alone can negate. It does not have to use do-support.
My preferred sentence would be:
We never had a lecture from this lecturer.