We present a real-time, fully automated method to remove instrumental signatures from stellar scintillation images. The method was developed in connection with the Low Layer SCIDAR (Scintillation Detection and Ranging) (LOLAS), an instrument dedicated to the measurement of atmospheric optical-turbulence profiles, C²ₙ (h), in the first kilometre of altitude, with high altitude-resolution. By examining the scintillation images and their correlation maps we evaluate, and then correct, image deficiencies typical of a portable telescope, such as defocus, image movement, field rotation and tracking errors, prior to processing according to the SCIDAR technique. In addition, detector spreading noise is corrected for, and flux variations caused by clouds or fog are monitored. The efficiency of the methods is demonstrated by comparing double-star scintillation autocorrelations obtained with and without the use of the self-adjusting procedures. Applying those stabilization methods, LOLAS was successfully exploited to characterize the C²ₙ vertical profiles along the lower layer on top of Mauna Kea Observatory.