How important is it, exactly, to use a rubric for grading undergraduate lab reports?
Having a rubric will make your own work grading fairly simpler, in particular if what you are grading are reports/essays. It breaks down your mental process of coming up with a grade. For example, if you don't have a rubrik, you may have to think about whether as a whole the report should be worth 70 or 75 points. There are many dimensions involved, and you will find that you are juggling too many balls when trying to assess how 3 or 4 reports compare to each other. It's easier if you only have to assess them on one dimension, e.g., spelling/grammar, use of examples, clarity of exposition, correctness of formulas used, adequacy of citations. You would then assign a grade for each report for each of the categories in your rubrik, and the task of computing an overall grade is only one of adding up the points.

A rubrik will also make your life easier when students (as they always do) come to your office hours and ask why they got this grade and not that. If you grade based on a holistic view, it's often difficult to articulate how you arrived at a particular grade. It's easier if you can break the grading down for the student into individual categories. You make your argument why you gave the student a 70 instead of a 75 a lot easier if you can explain why they only got a 10 out of 20 in grammar, etc.