How hard is it for a teaching-oriented lecturer to get tenure in mathematics in the United States? My questions is different from this post.
Suppose a math's PhD is 

1) not very successful in his PhD program research and fails to find an ideal postdoc.(But he is still eligible to gain a PhD degree)    or,
2) not very successful in his research as a postdoc and fails to find a tenure-track position like an assistant professor.

and he chooses to be a lecturer for a couple of years just to get rid of the heavy pressure of publishing papers but he is still ambitious about becoming a mathematician. My question is, is it extremely difficult for a teaching-oriented lecturer to get a tenure-track position in mathematics(assistant professor at least)?  
BTW, the only example I know about this is Yitang Zhang, whose experience was so special. But in general, I don't know any other examples of a lecturer becoming an assistant/associate professor in U.S.
 A: Not all tenure-track positions have research expectations (e.g. at schools where research is not a focus), but most do.  And in such cases, one of the hiring requirements is usually something like "evidence of potential for success in research".  By far the best evidence of future potential is evidence of recent past success.
So the "lecturer" title isn't necessarily the obstacle, but if this person has not been doing or publishing research during that time, and their research record prior to that is not impressive, what reason does a hiring committee have to expect that they would be successful in research in a tenure-track job?
If the person has been doing successful research during their time as lecturer, that is a different story.  But that seems counter to your suggestion that they took the job to escape the pressure of research.  It's also a difficult thing to accomplish in general, even for someone who is highly motivated: a lecturer job will not typically leave one much free time for research, and it may not include the sort of research support that a tenure-track job might (travel funding, graduate students, etc).
A: There are a lot of 2-year and 4-year colleges in the US where nowadays the mathematics department prefers to hire Ph.D.s, but where no research is required for promotion and tenure.  So I may disagree with Nate's "most" assertion.  
Now, if you still intend to do research, though: Such places probably have greater teaching duties than a research university, leaving you less time to do research.
