Is it useful to include my teaching experience in primary school when applying for lecturer position
I'd say that if it's the (only) teaching experience you have, you should probably mention it. Teaching is teaching. Regardless of the level at which you teach there are some basic skills which are common to most, if not all, scenarios. For example one expects teachers at all levels to be pedagogical. Moreover you'll be telling the selection committee that you are familiar with the job type, albeit at a different level. Indeed you know how to prepare a lesson, you have an idea of how the marking process works, you know how to keep students interested, etc.

Another important point to note is that primary school teaching experience shows that you were deemed competent, and responsible, enough to be allowed to work with kids, which is something I believe can say a lot about you. We all know how protective parents are with their little ones. Allowing you to somewhat shape the initial part of their lives definitely implies trust and recognition.