The necessary measurements for ordering a custom made leather strap (the only option, as the leather straps from IWC for other Ingenieur models won't fit) for an IWC Ingenieur Misson Earth are as follows:
Lug width: 31 mm (strap width at lug end: 31 mm) Strap width at narrow end: 20 mm IWC Springbar width: 1,5 mm in the complete length of 20 mm Due du the inverted lugs, there will be a cut out section on the lug end of the strap with a length of 16 mm and a depth of ca 3 mm Watch case length including lugs: 55 mm Length of original rubber strap: 115 / 75 mm Thickness of original rubber strap: 3 mm Width of original strap hooks: 5 mm
In addition I'd recommend taking good photos of the lug arrangement, of the entire strap stretched out and of the caseback for the strap maker to get a good idea of the original design.