Your diagram shows the truss having two short tethers that join a little way above it [the truss] and then a long single tether up to the balloon. I'd suggest using two long tethers direct to the balloon instead.
The reasons for this are that a long single tether will have very little resistance to twisting and will be prone to winding itself up and, in addition, will also be more prone to penduluming/swinging.
The result of wind-up will be spinning of the truss (in the horizontal plane) and swinging is also undesirable as it will be changing the angle at which LOHAN is actually launched. Twin tethers won't stop this entirely, of course, but it should reduce it somewhat.
Dunno what you're planning to use for the tethers but something non-stretchy would be a good idea: consider some heavy-test Dacron fishing line i.e. the stuff they use for marlin and sailfish sport fishing.