I was thinking maybe this might work, since I could not think of another way for the other suites to not execute.
Have a Test Suited with a Test case I know will fail.
Have another Suite:
Create a new test case that calls the suites with REST steps that calls lisa-invoke:
First step:
I create an XML XPath Assertion to look at the fail count that comes back from lisa-invoke if the Suite fails:
If there is a failure, then the next step does not get executed, the test ends there.
Others might know of a better method, but thought this might work.