Generally, once you miss a leg on a ticket, they cancel the rest of the ticket, so you could use only the outbound, but not only the inbound; this won't solve your problem.

You should call LX and see about discounted one-ways. The one-way is probably more expensive because it's a higher fare bucket, and often the higher fare buckets do have child or adoption (I don't know if this would be considered such) discounts.