To my knowledge there has been no research about treating children who clutter using the Lidcombe Program. In fact, cluttering is often not diagnosed until a child is beyond the preschool years (St. Louis et al 2007). For these reasons much of what I say here is based on clinical observations rather than on published evidence.
If a child has a clutter as well as a stutter there may be a variety of impacting factors to consider including language or learning disorder, a fast speech rate, compromised intelligibility, and poor self evaluation. I would suggest treating the stuttering first, as you would with the Lidcombe Program, but ensure that verbal contingencies are only applied to effortless, stutter-free and intelligible speech. If the stutter is successfully treated but the cluttering behaviours remain, they may need to be treated separately.
It is difficult to predict what will happen in the case of this little boy. The most logical course to undertake would be to treat this child as a single case study. Take very careful measurements prior to and during treatment. Base your clinical decisions on these measures. Seek supervision opportunities and problem-solve this unusual case with senior staff or mentors.
Finally, consider writing up this case study for others to learn from your experience of treating a preschool age child who clutters.
St. Louis, K. O., Myers, F. L., Bakker, K. & Raphael L. J. (2007). Understanding and treating cluttering. In Conture E. G. & Curlee R. F. (Eds.), Stuttering and related disorders of fluency (3rd ed.) (pp. 297-322). New York: Thieme.