TG should have automatically protected the passenger following the misconnect into Bangkok. This is likely to mean accommodation on the next TG service to ZRH, which means an extended stay in BKK. (Unlkely TG will accommodate on another airline, or rebook via another TG port with a connection to ZRH.)
LM will only be able to reacommodate the passenger if there is award seating available on the replacement flight. If there are no award seats, TG will have to transfer a revenue seat to an award seat, and transfer the passenger accordingly. LM will need to accept the changes and make sure the ticket is on order.
I would first check the LM site to see if there are alternative award seats available. This will be the quickest method. Make sure the change fee is waived.
If there aren't any award seats, try calling TG at first instance, making it clear that their schedule change has caused the misconnect. If they give you the run-around, email them instead (that'll give them time to properly consider the issue).
In either event, make sure LM correctly accepts any changes to the ticket. Without a valid ticket, carriage may be refused.
Whether or not TG will also pay for a hotel is another issue. I seem to recall this matter being discussed previously? Not sure of the outcome.