Colorectal cancer (CRC) is among the most malignant pathologies worldwide. A major factor contributing to the poor prognosis of neoplastic diseases is the development of drug resistance. It significantly reduces the utility of most therapeutic protocols and necessitates the search for novel biomarkers and treatment strategies to combat cancer. An evolutionarily conserved catabolic mechanism, autophagy maintains nutrient recycling and metabolic adaptation and is also closely related to carcinogenesis, playing a dual role. Autophagy inhibition can limit the growth of tumors and improve the response to cancer therapeutics. Lysosomes, key players in autophagy, are also considered promising targets for anticancer treatment. There are still insufficient data on the role of poorly studied glycoproteins related to autophagy, such as the lysosome-associated membrane glycoproteins (LAMPs). They can act as multifunctional molecules involved in a multitude of processes like autophagy and cancer development. In the current review, we summarize the recent data on the double-faceted role of autophagy in cancer with a focus on drug resistance in CRC and on the roles of lysosomes and LAMPs in these interconnected processes. Several lysosomotropic drugs are discussed as options to overcome cancer cell chemoresistance. The complex networks that underline defined autophagic pathways in the context of CRC carcinogenesis and the role of autophagy, especially of LAMPs as drivers of drug resistance, are outlined.