Lumby will become managing director of Carillion's infrastructure services division next week, after the departure of Rowan Sharples.
John Moore, the former operations director of rival M&E contractor Semple Cochrane, will replace Lumby as MD of Crown House.
Carillion has appointed former Johnson Controls managing director Don Kenny as MD of its facilities management arm. This move will reunite Kenny with Carillion chief executive John McDonough, who joined from Johnson Controls last year.
A city analyst said Carillion had been reducing the size of its M&E business for a number of years as part of a group-wide refocusing on higher value contracts and sectors.
Crown House was too big in relation to the rest of the firm
He said: "Carillion thought Crown House was too big in relation to the rest of the group, and not something it wanted to be doing as much of." He added that it was no surprise that Lumby had moved on, as he had been fast-tracked through the firm and was tipped as a future main board director.
In August 2000, 900 redundancies were made at Crown House after group restructuring and a shift away from high-risk and smaller contracts.
Losses at the firm and the cost of the redundancies resulted in a £34m exceptional charge in the year-end accounts. The move led to a drop in turnover of one-third to £150m.