I don’t really know LSL, but from the description on Wikipedia, you define in it a finite state machine, defining which computation is done in each state.
If I’m not mistaken, Turing completeness is defined by five characteristics :
- Ability to read variable values
- Ability to write values in variables
- Ties/unconditional deviation
- Decision-making structure
- Ability to perform operations with read/stored variables
(Citation needed, I saw it in computability class about seven years ago).
Thus, even more since I have not seen anything that prohibits recursion on LSL, I believe it is complete. A "simple" test is to try to write a Turing machine interpreter.
EDIT
Do not confuse robust programming language with full Turing language. Brainfuck is complete but even so it can be considered robust as a language for commercial use.
EDIT 2
More about Turing completeness in that reply from Maniero. Excerpt that I found interesting from his answer to that particular question:
- store - and read obviously - data somewhere at least transiently - maintain status (not I/O);
- transform data to express the simplest mathematical operations (I would say that addition and multiplication in their most basic form are necessary);
- maintain a "run" sequence - logically organize the stores and transformations;
- divert the sequence;
- take a decision between at least 2 "paths".
I have some disagreements about item 2 (if my understanding was what he really intended to express), because with the unary numbering system it is possible to write the sum operation and, from it, multiplication and subtraction.