I had been running a guide on (Luther/NABRE notation) Joel 4:16 - not many results - and opened some bibles, lastly NABRE. Tried to switch the guide to a larger section when Logos became unresponsive. The Log says in a warning that at 20:05 process 1 couldn't find where to place the focus and set it somewhere - but it no longer reacts to me. Another process happily synchronized some stuff and at 20:09 yet another process logged a (quite usual on my machine) web exception warning. At this time I already was looking for the Hang. No further activity is written to the log since then, no errors. No crash or something, thus no crashlogs, the last error was prior 18:00 in another session and the last indexer run finished around 19:30 which was the library preparation.
Screenshot of frozen L5 (I was running the German UI, the media lookups were not moving):

Task Manager still things the application is normally executed.
And now - while I was writing this post, made a screenshot of Taskman and just wanted to look into Resource Manager - it starts working again!
These are consecutive lines from the log:
2014-07-31 20:05:21.5872 1 Warn ElementUtility Unable to set focus to default focus: DisplayPane (OurDisplayPane) <- Grid <- DockPanel (OurDisplayPaneGrid) <- Grid (ResourceContent) <- Grid (ContentGrid) <- Border <- ContentPresenter <- Grid (TheContentWrapper) <- Grid (TheGrid) <- Border <- PanelView (ResourcePanelView) <- ContentPresenter <- TiledFramePanelContent <- ContentPresenter (PART_SelectedContentHost) <- StatusBarDecorator (PART_StatusBarDecorator) <- Grid <- OurTiledFrameTabControl <- TiledFrameGrid <- OurTiledFrame (TheMainFrame) <- Grid (TheClient) <- IndexedPanel (HomeClientLayout) <- Grid <- Border <- Border <- DockPanel <- ContentPresenter <- AdornerDecorator <- Grid <- Border <- DockPanel <- Border <- Canvas (PART_Canvas) <- MainWindow
2014-07-31 20:05:21.5932 1 Info ElementUtility Couldn't find default focus; focus set to first focusable item.
2014-07-31 20:05:22.2042 19 Info SyncClient (781ms) Submitting 1 of 1 items.
2014-07-31 20:05:22.2352 19 Info SyncClient Integrated 1 successes, 0 conflicts, and 0 errors.
2014-07-31 20:05:22.2382 19 Info SyncClient Downloading items for HistorySyncItem
2014-07-31 20:05:22.4982 19 Info SyncClient New last known milestones: {"itemMilestone":"16662"}
2014-07-31 20:05:22.5412 19 Info SyncManager Finished requesting sync on all sync clients. Summary of elapsed times:
2014-07-31 20:05:47.6036 19 Info SyncManager Requesting sync on all sync clients
2014-07-31 20:05:48.9057 19 Info SyncClient Downloading items for PreferencesSyncItem
2014-07-31 20:05:49.6048 19 Info SyncClient Unchanged last known milestones: {"itemMilestone":"1000484879"}
2014-07-31 20:05:49.6478 19 Info SyncClient Downloading items for ReadingProgressSyncItem
2014-07-31 20:05:50.3748 19 Info SyncClient Unchanged last known milestones: {"itemMilestone":"44630894"}
2014-07-31 20:05:50.3838 19 Info SyncClient Found 1 items to submit for HistorySyncItem
2014-07-31 20:05:50.3858 19 Info SyncClient (Timed) Submitting 1 of 1 items.
2014-07-31 20:05:51.0948 19 Info SyncClient (709ms) Submitting 1 of 1 items.
2014-07-31 20:05:51.1168 19 Info SyncClient Integrated 1 successes, 0 conflicts, and 0 errors.
2014-07-31 20:05:51.1328 19 Info SyncClient Downloading items for HistorySyncItem
2014-07-31 20:05:51.4749 19 Info SyncClient New last known milestones: {"itemMilestone":"16663"}
2014-07-31 20:05:51.5279 19 Info SyncManager Finished requesting sync on all sync clients. Summary of elapsed times:
2014-07-31 20:06:45.0319 19 Info SyncManager Requesting sync on all sync clients
2014-07-31 20:06:46.2180 19 Info SyncClient Found 3 items to submit for ReadingProgressSyncItem
2014-07-31 20:06:46.2360 19 Info SyncClient (Timed) Submitting 3 of 3 items.
2014-07-31 20:06:47.0570 19 Info SyncClient (820ms) Submitting 3 of 3 items.
2014-07-31 20:06:47.0760 19 Info SyncClient Integrated 3 successes, 0 conflicts, and 0 errors.
2014-07-31 20:06:47.0920 19 Info SyncClient Downloading items for ReadingProgressSyncItem
2014-07-31 20:06:47.3501 19 Info SyncClient New last known milestones: {"itemMilestone":"44630895"}
2014-07-31 20:06:47.4031 19 Info SyncManager Finished requesting sync on all sync clients. Summary of elapsed times:
2014-07-31 20:06:47.9061 19 Info SyncManager Requesting sync on all sync clients
2014-07-31 20:06:48.9751 19 Info SyncClient Downloading items for ReadingProgressSyncItem
2014-07-31 20:06:49.6822 19 Info SyncClient Unchanged last known milestones: {"itemMilestone":"44630895"}
2014-07-31 20:06:49.6922 19 Info SyncClient Downloading items for HistorySyncItem
2014-07-31 20:06:50.6192 19 Info SyncClient Unchanged last known milestones: {"itemMilestone":"16663"}
2014-07-31 20:06:50.7042 19 Info SyncManager Finished requesting sync on all sync clients. Summary of elapsed times:
2014-07-31 20:09:28.6043 7 Warn HttpWebRequestUtility WebException reading WebResponse from 'https://www.logos.com/product/105/thumb/alone-with-god.jpg?': Timeout für Vorgang überschritten
2014-07-31 20:30:39.5810 1 Info PanelViewModel Got panel settings for History: Key=SermonTheme%7cref%3dbible+einheit.29.4.1-29.4.21|TemplateName=SermonStarterGuide
2014-07-31 20:30:39.6600 1 Info LDLS4.AppModel App is now idle.
2014-07-31 20:30:43.8922 1 Info LDLS4.AppModel App is no longer idle.
2014-07-31 20:30:43.9002 1 Info PanelViewModel Got panel settings for Preferences: Key=SermonTheme%7cref%3dbible+einheit.29.4.1-29.4.21
2014-07-31 20:30:43.9342 1 Info MainWindow MainWindow activated.
Logfile: 1256.Logos (2).zip