I thought the BBC was already committed to Adobe Première as part of their "Creative Desktop Initiative"
www.broadcastnow.co.uk/technology/bbc-commits-to-premiere-pro/5018203.article
Lightworks would need interface with their system get a toe hold into the BBC though pressure from the programme making staff staff really wanting to use it instead or AVID or FCP. However, I suspect Lightworks may be more about keeping keeping editors in the outside world happy than keeping BBC corporate suits feeling safe in their jobs.
Also, to be really at its best Lightworks needs a console, that's not saying you need one to edit extremely well, but for Lightworks to be used to its max. That may be an extra cost, although I'd imagine the BBC would strike a deal for a large order.