Will an iphone in lost mode enable celular data on its own?
In short - if your device doesn't have cellular, the lost mode transmission won't be received until / unless it rejoins or connects to the internet via WiFi or someone puts in a working SIM chip with compatible data plan.

This link may help you determine the answer to that question.

https://support.apple.com/kb/PH19299

In this article, you will see the following. Hopefully this answers your question.


  
  If you used Lost Mode, when tracking begins, you see your device’s current location, as well as any changes in its location on the map.
  
  If your device is online  when
  you put it in Lost Mode or lock it, it locks and tracking begins (if
  applicable). If Location Services is turned off on the device, it’s
  temporarily turned on to track your device’s location. A confirmation
  email is sent to your Apple ID email address.
  
  If your device is offline ,
  the passcode lock and tracking (if applicable) take effect the next
  time it’s online.