I do not know the LSL background, but by describing it in the Wikipedia , you define in it a finite state machine, defining computing is done in every state.
If I'm not mistaken, turing completude is defined by five characteristics:
Ability to read variable values
Ability to write values into variables
Ties / unconditional deviation
Decision structure
Ability to perform operations on read / stored variables
citation needed , I saw it in computability class about seven years ago).
So, even more that I have not seen anything that forbids recursion in LSL, I believe it to be complete turing. A "simple" test is to attempt to write a turing machine interpreter.
EDIT
Do not confuse robust programming language with full turing language. Brainfuck is full turing, but even so it can not be considered robust as a language for commercial use.
EDIT 2
More about Turing completeness on this Bigown answer . Excerpt I found interesting from his answer to that particular question:
- store - and obviously read - data somewhere at least temporarily - maintain state (not I / O);
- transform data in order to express the simplest mathematical operations (I would say addition and multiplication in their most basic form are necessary);
- maintain a "run" sequence - logically organize stores and transformations;
- divert sequence;
- Make a decision between at least 2 "paths".
I have some disagreements regarding item 2 (if my understanding was what it was really intended to express), because with the unary numbering system it is possible to write the sum operation and, from it, multiplication and subtraction.