LX is not a community carrier. The Swiss law enactment of what is EC 261/2004 in the EU, applies to this ticket because the delay occurred on a Swiss carrier between a point outside Switzerland and Switzerland. The fact that OP had onwards tickets to the UK won't matter. Even if one looks at this as a SIN-LHR ticket, it is still not a UK carrier.
Just because there may be an ability to file in a UK court does not mean that UK, e.g. EU law, applies.
Traveling in the other direction, e.g. LHR-ZRH-SIN, LX would likely deny a claim if the ZRH-SIN segment had been cancelled for the same reason and then concede if sued in a UK court because, in that instance, EC 261/2004 would apply because this would have been a ticketed connection departing the EU.
Yet another issue here is that OP had a stopover, not a connection at ZRH. Even a most extreme reading of the current UK case does not extend to a stopover which is an intentional break in travel rather than a connection.