Decomposing mulch already adds nutrients to your soil. Adding new mulch will regain the ability to hold water and prevent weeds.  I am not sure what you hope to gain by adding compost. It can raise the pH. If you do add compost be sure that it is properly aged rather than farmyard compost because that compost can contain weed seeds. It’s probably not a good idea given your soil pH.  

Probably a better idea is to fertilize your landscape beds around plants. Mulch should never touch the stems of plants. It should be pulled back 6-8 inches to prevent pests and prevent mulch from pulling water from the plants. You could place the compost in those areas next to the plants or just use regular fertilizer around the plants.

See:  https://www.canr.msu.edu/news/build_smart_soils_using_mulch_composted_organic_matter_and_reducing_tillage

Without seeing the rest of your soil test, especially the type of soil (sandy, loam, clay) and the fertilizer recommendations, it is hard to make a recommendations for your lawn. As for lowering the pH of the lawn, this will be a long process.  You can only add so much sulfur at one time and it is best done now in the early spring.

Coffee grounds do not lower pH, so the more dilute coffee would not either.  See:  https://extension.umn.edu/manage-soil-nutrients/coffee-grounds-eggshells-epsom-salts

There are other possibilities. Instead, you may be better off slightly increasing the annual nitrogen, phosphorus, potassium, and possibly iron applied to the turf. (https://turf.purdue.edu/sulfur-is-not-effective-for-lowering-ph-of-turfed-soils/)

Finally, your lawn pH really isn’t high enough to worry about. But if you feel you must do something the above websites can give some guidance.