Try out something like meguiar's clay bar or some such. Also, for lubricant, their quick detailer or something like Adam's detail spray I have noted below while claying works best for me. Also, when claying, I have found that after making a couple passes, if the clay has dirt in it, is discolored, or something similar, I use a hand slicer like below to remove the contaminants quickly.
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https://smile.amazon.com/dp/B001QVGUMO/ref=sspa_dk_detail_0?psc=1
https://smile.amazon.com/dp/B001QGPHXM/ref=psdc_289783_t2_B0090JINY2