Couldn't stop fiddling:
(1) as I have already written: rollback to Lemmings works
(2) searchindex-plugin freshly installed, it also works (although "vector"-template didn't show rebuild button and complained about missing Java, tried "default"-template again and "rebuild"-button appeared, after changing back to "vector"-template the rebuild button appeared there as well ... the refresh-button would probably have worked as well). After pressing the rebuild button, the plugin crawled through the files and sucessfully rebuild the index.
(3) deleted and reinstalled the tag-plugin, hacked the plugin's script.js to resolve incompatibility with searchindex (
http://github.com/dokufreaks/plugin-tag/commit/a200db358f84ad1c5b9049c7a30046e3ecae99c2). Result: Tags are displayed, Tag-Index can be rebuild, and the edit buttons "reappear" (i.e. the incompatibility with searchindex is resolved by hacking the plugin's scripts.js)
=> I successfully get Lemmings to work with searchindex and tag plugin
I will now go back to give "Lazy Sunday" a try ...