Trifid Cipher (without keyword)
Charcoal, 39 bytes

≔Ｅ⁺θ× ¬﹪Ｌθ³⌕βιθ⭆⪪Ｅ⁺÷θ⁹⁺÷θ³θ﹪ι³¦³§⁺β ↨³ι


Try it online! Link is to verbose version of code. Explanation:

≔               Assign
   θ            Input string
  ⁺             Concatenated with
                Literal space
    ×           Repeated
         θ      Input string
        Ｌ       Length
       ﹪        Modulo
          ³     Literal 3
      ¬         Logical not
 Ｅ              Mapped over characters
             ι  Current character
           ⌕    Position found in
            β   Lowercase alphabet
              θ To variable

     θ                      List of positions
    ÷                       Vectorised integer divide by
      ⁹                     Literal 9
   ⁺                        Concatenated with
         θ                  List of positions
        ÷                   Vectorised integer divide by
          ³                 Literal 3
       ⁺                    Concatenated with
           θ                List of positions
  Ｅ                         Map over values
             ι              Current value
            ﹪               Modulo
              ³             Literal 3
 ⪪                          Split into
                ³           Groups of 3
⭆                           Map over groups and join
                   β        Lowercase alphabet
                  ⁺         Concatenated with
                            Literal space
                 §          Cyclically indexed by
                       ι    Current group
                     ↨      Converted from
                      ³     Base 3
                            Implicitly print