Swiss doesn't fly to Vietnam. Thai (I assume) was the carrier to fly you there on the final leg from BKK, and therefore, they're responsible*.
*It's always the last carrier that is responsible for the search of missing/lost baggage, including payments. If LX lost the bag already within their area of responsibility, then TG could later claim back money from them, but that's not the concern of the customer, but intra-airline stuff.
Basically, TG should have compensated you (reasonable expenses for clothing, personal items etc.) and IF it later came out that LX made a mistake, claim whatever they paid to you from them.
Very possibly, the luggage got lost while in transit in BKK.
Thus, LX had close to none access to whatever data from Thailand, and even if they had, TG would still be responsible.
Did the staff on arrival in Vietnam not made this clear to you, that TG is fully responsible, and not LX?
Basically, I totally understand that you were angry, but you're yelling at the wrong desk here.