This may be potentially a potentially useful datum in this saga. I will leave it to those more knowledgable than I to ponder the implications.
I run two nearly identical iMacs (hereafter denoted iMac I and II), both on OS 10.7. I recently downgraded iWork on iMac I back to Keynote 5.05. Everything runs well as described above, albeit without autosave. In the process, I executed a "Verify Disk" on the startup volum (Macintosh HD) with Disk Utility. It detected disk errors that needed repair. I rebooted iMac I with the alternate partition (Command-R on Restart) and repaired the startup volume using Disk Utility. This seemed to clear up a lot of pesky little issues I've had recently with WiFi connectivity, internet, and network connections to Airport Express, none of which are relevant to this thread but interesting to note.
Now to iMac II. I verified that the startup volume Macintosh HD had no disk errors according to Disk Utility. Keynote 5.1 seems to run perfectly well on OS 10.7 on iMac II. To verify this, I brought over a copy of my most troublesome, crash-prone, beach ball spinning Keynote file, a whopping 512 MB with 7 imbedded videos in various formats. After repeated attempts to either crash, burn and/or volley the endless beach ball of doom, I can attest that Keynote 5.1 does indeed work with OS 10.7 on iMac II. (A friend who did a clean install of OS 10.7 on his laptop corroborates this with his own Keynote experience.)
What remains for me to do, in true Mythbusters fashion, is to update iWork on iMac I and return to Keynote 5.1 now that the startup volume disk errors have been corrected. I will report back the results.
In the meantime, those who are having Keynote 5.1 issues on 10.7 may want to run Disk Utilities on the startup volume (not the hard disk but the volume labeled Macintosh HD). If it detects any errors, run the repair cycle as described above. It's easy, it's foolproof, and you have nothing to lose.
Perhaps the problem was with the Lion upgrade and not the iWork update. But that diagnosis is beyond my knowledge.