Launderettes were never as popular in France as they were, at one time, in the UK. So finding one there is even harder than it is nowadays here. The nearest I can find is this one, which is 4km from your hotel. (Bus number 22 gets you most of the way):
http://www.laverie-lyon.fr/lyon-2.htm
Transport information here:
http://www.tcl.fr/en
That launderette is close to
Carrefour Lyon Confluence
112, cours Charlemagne
69002 LYON
where you should be able to get most of the items on your shopping list fairly cheaply.
Alternatively, try the big Auchan store near to the airport:
http://www.auchan.fr/magasins/lyon-porte-des-alpes/32/informations-pratiques/