The background: I'm a postdoc in mathematics (U.S.) and approaching the end of my postdoc term. I applied for permanent academic jobs last fall and did not end up getting a tenure-track job offer. It was somewhat surprising; I have a very good publication record, in both quality and quantity (e.g., regular papers in "top 20" pure math journals). As recently as a month ago, it seemed that my academic career was over. But I was fine with it---I also got an offer for a good non-academic job (though it is currently unofficial; it will be some time before I get an official offer).
The situation suddenly changed when I learned that my NSF grant application (the standard 3-year research grant) from last fall had been funded! I talked to my postdoc institution about the situation, and they have decided to let me extend my postdoc another year so I can apply again for jobs in the fall. A couple weeks later, I was unexpectedly contacted about an open non-tenure track teaching-oriented lecturer position at another university and quickly offered the position. It's a good offer (aside from the detail of not being tenure-track), though it would be an unusual situation to hold it as an NSF-funded researcher.
In summary, I have three options: (1) take the lecturer position; (2) stay put at current institution another year and apply again; (3) hold out for the non-academic job. I'm inclined to take the lecturer position, but I also wonder if this would be a career-limiting decision. If I stay in academia, it is with the goal of getting a tenure-track job, so I want to get a sense of what is the most viable path forward.
Here's my question: how much upward mobility does a person generally have after taking a lecturer position? That is, should I expect the chance to land a tenure-track job at a future point, or will I effectively be out of contention?
And the answer should be weighed relative to the alternative of extending the current postdoc.