While LX and SQ are Star Alliance members, in order to have baggage checked through to destination, you actually need both flights on the same ticket.
Separate to that,
SQ and the
LH group which include LX have a Joint Venture Agreement but the benefits of the JV usually extends to single ticket travel only.
JV Agreement
That said, Changi has transfer desks, and in the past it has been possible for transit passengers on separate tickets to approach the transfer desks to ask then to retrieve and retag the baggage without the passenger having to clear immigration, pick up baggage and recheck.
There are transfer desks in each terminal.
So, in short, there is no guarantee that your baggage will be checked through to DPS but there are 2 possibilities- ask check in at ZRH, and failing that, ask the transfer desk at SIN Terminal 2 (generally this is the arrival terminal for LX at SIN). In any case you may have to visit the Transfer Desk if you are unable to get a Boarding pass for the SIN-DPS sector.
Star Alliance advice:
Changi Airport advice:
Picture of one of the Transfer Desk
