I am quite certain, given the number of different lysosomal storage diseases, that there is not a generic QoL questionnaire. The only one with which I am really familiar is that for Fabry disease.
Yes, the SF-36 has been used for some time in gaucher disease type 1.
Qual Life Res. 1999 May;8(3):263-8.
Quality of life assessment in adults with type 1 Gaucher disease.
Masek BJ1, Sims KB, Bove CM, Korson MS, Short P, Norman DK.
The question of validation for all different forms of LSDs is complex bc the of the variability in phenotype, esp neuronopathic. How do you adequately assess a late MPS III QOL?