Thunderbolt Daisy Chain to Non-Thunderbolt Monitor w/LG 34UM95 at end of chain
It's doable, one simply must include a TB device between the two monitors.  

Computer->TB Monitor->TB Device->Non-TB Monitor 

The TB device can be any dock, drive, etc. that has TB-in and TB-out ports (2 x TB ports).


The technical details have to do with the way TB carries and decodes display signals.  TB can carry 2 signals.  Essentially, each TB device can only decode 1 x display signal (there's more to it, and technically TB devices could decode 2 signals, it just ain't happenin' right now).  So your initial TB monitor can decode one for viewing on itself and pass the other along...but it isn't decoded.  You need a second TB device to decode that second signal.  If the second device is a TB display, then you're in-like-Flynn.  If not (like in your case), you need another TB device to decode the signal before it hits your non-TB monitor.