I know that Lucene indexes cannot be shared:
Sitecore keeps a local copy of the Lucene index in the file system of each instance and does not suppor
You can also consider using the open source Sitecore Lucene Refresher that will run a index crawl operation in-memory and will commit the index back to the file system so you don't lose any index content during the rebuild process. This can at least help. Then maybe, set up some sort of agent to run this crawl/rebuild operation at a specific time of day to keep all CD servers doing this at the same time in-sync.