In the U.S., in math, at research-oriented universities, there are at least two sorts of "lecturers". (And, note, this title is entirely different from that in the UK.)
First, there is non-permanent, but long-term, contracted sort of adjunct faculty, whose duties are exactly teaching, nothing else. There is not a progression to assistant professor, etc. It is not at all tenure-track.
Second, analogously, there are explicitly temporary versions of "lecturer", to fill teaching needs. No long-term commitment at all. Similarly for more elevated titles (and pay?), but no long-term commitment: visiting assistant prof, visiting X.
Third, there are some fancier "lecturer" or "instructor" positions intended as approximately post-docs, sometimes with honorific names attached. So-and-so instructor/lecturer in mathematics. But, again, no long-term commitment.
And, as @Buffy says, these days there is usually a legal requirement to conduct a well-advertised nation-wide search for any tenure-track position. Since lecturers/instructors are usually not in the pipeline for tenure at a given place, they have to compete with everyone else. Sure, it's good to have cultivated good-will and appreciation, but that's not a guarantee.
(So, most likely, if you have a lecturer/instructor position for a year or two, you'll be back to the same spot at the end, of applying for tenure-track positions all over again, with no promise that the place that made the offer this year will make you another one that year.)