One of the sacked contractors told CW360.com that most of the dismissed workers have been working on the project for the past seven years.
Lockheed Martin has replaced the sub-contractors - who were employed by Thales ATM - with its own staff.
Thales was working on Workstation Display Manager software, which draws radar displays and presents flight information to air traffic controllers, under a sub-contract with Lockheed Martin.
Thales' regional director, Richard Moore, told CW360.com: "It is quite true that Lockheed Martin has advised us that they won't require our support on that activity [the Swanwick project].
"Lockheed Martin has put its own staff in. But whatever happens, this programme is coming to an end," he added.
The situation appears to have arisen from the fact that Thales is Lockheed Martin's primary competitor in a bid for the contract to carry out similar work in Prestwick, the site of the New Scottish Centre (NSC) air traffic control site.
Prior to the privatisation of NATS earlier this year, Lockheed Martin had been told it could have the contract for the NSC. However, it is now being forced to put in a competitive tender.
Moores admitted that bidding for the NSC contract has influenced the situation. "We recognised that because NATS didn't want [Lockheed Martin] doing the contract. We won't be supporting them as a sub-contractor," Moore said. "This may seem like bad news, but in the long term NATS is going down the competitive road, which is very positive."
Lockheed Martin refused to talk to CW360.com on the grounds that it is forbidden to do so under its contract with NATS.