Trek ran low-cost services between Johannesburg and Luxembourg. They couldn't get licences into any decent destination in Europe because the mainstream carriers would lobby against this, but Luxembourg had no home carrier to Africa. The same approach applied to Loftleidir coming from the USA. My guess would be that they were at Amsterdam for maintenance, this not being so readily available in Luxembourg.
It took the Viking (which is essentially a WW2 Wellington with a new fuselage, and thus familiar to many crews and engineers in the 1940s-50s) four days, with leisurely overnight stops in hotels, even with opportunities for sightseeing, and the same crew throughout. Services were typically weekly, needing two aircraft. Trek had three Vikings from 1955-59, even much later in their 707 and then 747SP days they did little else. The Vikings were picked up from UK independents, and later sold on to African residual operators. Here's the route
http://www.timetableimages.com/ttima...b/tre50sb1.jpg
Wasn't the only long haul Viking route to Africa at the time. Central African Airways did Salisbury, Rhodesia (now Harare, Zimbabwe) to London, while UK independents Hunting-Clan and Airwork both did similar operations from London (typically Blackbush) across Africa. Most of these were also once-weekly operations, and despite the hotel and stop costs, and low passenger numbers, were significantly cheaper (less than half) what BOAC charged.