The functions of mammalian Atg8 proteins (mATG8s) expand beyond canonical autophagy and include processes collectively referred to as Atg8ylation. Global modulation of protein synthesis under stress conditions is governed by MTOR and liquid-liquid phase separated condensates containing ribonucleoprotein particles known as stress granules (SGs). We report that lysosomal damage induces SGs acting as a hitherto unappreciated inhibitor of protein translation via EIF2A/eIF2α phosphorylation while favoring an ATF4-dependent integrated stress response. SGs are induced by lysosome-damaging agents, SARS-CoV-2 open reading frame 3a protein (ORF3a) expression, Mycobacterium tuberculosis infection, and exposure to proteopathic MAPT/tau. Proteomic studies revealed recruitment to damaged lysosomes of the core SG proteins NUFIP2 and G3BP1 along with the GABARAPs of the mATG8 family. The recruitment of these proteins is independent of SG condensates or canonical autophagy. GABARAPs interact directly with NUFIP2 and G3BP1 whereas Atg8ylation is needed for their recruitment to damaged lysosomes. At the lysosome, NUFIP2 contributes to MTOR inactivation together with LGALS8 (galectin 8) via the Ragulator-RRAGA-RRAGB complex. The separable functions of NUFIP2 and G3BP1 in SG formation vis-a-vis their role in MTOR inactivation are governed by GABARAP and Atg8ylation. Thus, cells employ membrane Atg8ylation to control and coordinate SG and MTOR responses to lysosomal damage.Abbreviations: Atg8: autophagy related 8; ATG: autophagy related; ATF4: activating transcription factor 4; EIF2A/eIF2α: eukaryotic translation initiation factor 2A; GABARAP: GABA type A receptor-associated protein; G3BP1: G3BP stress granule assembly factor 1; LLOMe: L-leucyl-L-leucine methyl ester; LysoIP: lysosome immunopurification; mRNA: messenger ribonucleic acid; MTOR: mechanistic target of rapamycin kinase; NUFIP2: nuclear FMR1 interacting protein 2; ORF3a: open reading frame 3a protein; SARS-CoV-2: severe acute respiratory syndrome coronavirus 2; SG: stress granule; TIA1: TIA1 cytotoxic granule associated RNA binding protein.