
It must be somewhere on the FamilySearch site. Look for Šiauliai county (Шавельский уезд). While I'm reading through sources online, I put them with descriptions into this project:
https://www.geni.com/projects/Census-in-Lithuania/4484567
I checked on the LitvakSIG site as I donate to the District Research Group for Siauliai. The 1816 RL has not been scanned/translated/indexed by LitvakSIG, which suggests that it is not available.
Here's what they do have:
1765, 1784 GDL Poll Tax lists (no surnames)
1825, 1834 etc RLs
You should write to Jody Tzucker, who is the DRG coordinator for Siauliai District. I'll send you her email in Geni email.