Gregorian to Noxu Time System Conversion
APL, 87

t[3]←(1+3⌷t←137 91 4 100⊤⍎2⍕⎕÷864)⌷'Looplab' 'Sevit' 'Hexteria' 'Sinpad'
'  '⎕R'-'⍕t


APL has an advantage in these time system conversion challenges due to the built-in encode function, at the cost of expensive string manipuation

Explanation
(using 1357510372 as example)

⎕÷864 takes user input from screen, divide by 864 (1571192.56018519)
⍎2⍕ and round to 2 dp.  (1571192.56)
137 91 4 100⊤ Then, converts to Noxu Time System (43 14 3 92.56)
t← and assign that to variable t.
1+3⌷ take the 3rd item from t, add 1 to account for 1-based indexing, (4)
(...)⌷'Looplab' 'Sevit' 'Hexteria' 'Sinpad' convert to Skizzle name, (Sinpad)
t[3]← and finally plug back into the 3rd item of t.

⍕t Convert t to a string representation, (43 14 &nbsp;Sinpad &nbsp;92.56)
'  '⎕R'-' and replaces 2 spaces with a dash (43 14-Sinpad-92.56)