How can the life time of a multiple star system, such as for example the trinary system PSR J0337+1715 be derived?
Such a three-body system is in principle expected to show a chaotic behavior sooner or later. Nope. Hierchical multiple systems (such as this), where the semi-major axes differ by a factor ten or larger may well be stable for ever (never become chaotic), in particular if the eccentricities are low and if the most massive object is in a tight binary. 

An unstable three-particle system will eventually result in (typically) the two most massive objects in a tight binary and the third particle ejected (unbound). The time scale for this to happen is of the order of several (10-100) dynamical times and is indeed a highly chaotic process.

The concept of the Lyapunov time scale is not too useful here. One issue is that as soon as one object is ejected (unbound), the system is no longer bounded, when the concept of Lyapunov becomes problematic. Another issue is that the Lyapunov time is defined in the limit of infinite time and does not necessary reflect the behaviour of the system over any finite time.

Finally, to answer your question. I think there is no stringent way. What one can do is to integrate numerically many realisations of the system, each equally in agreement with the data (and their uncertainties). Then one can see whether there are any stable configurations and how frequent they occur. Given that the system didn't form yesterday, it appears likely that it is indeed stable.