Which recommender should I go for getting a LOR for graduate school admission?
In general, if you are applying for a research degree, then you are better off getting letters of recommendation from people who can comment on your ability as a researcher. Even if the person is a well-known expert in the field, that won't do them a whole lot of good if they can't comment on your abilities in the field.

Your department head has neither observed your work in classes nor supervised research for you. How much detail she can provide on your capabilities is therefore greatly in doubt. You have taken classes and performed research with the lecturer. Therefore, your lecturer can evaluate you more thoroughly and provide evidence supporting those claims. 

So, unless you have some additional absolutely compelling reason to obtain the letter from the department head, I would go with the instructor who actually knows your work.