Twin lamb disease itself is usually closer to lambing, I agree. My experience with the hypocalcaemia up north was that a) they didn't go on to develop TLD; they either got up within an hour of being treated, or died very quickly, and b) they could get it any time they were under severe physiological stress - so being pregnant plus a sudden change in the weather could do it, as could being gathered while pregnant, being disturbed by a dog they didn't know... it was harsh up there, so any additional stress could tip them over. We could and did get hypos from shortly after tupping right up to lambing. And often just found a dead ewe, no sign of anything wrong, no loss of condition, etc, and assumed that many of them would have gone hypo after the previous check and died before being found. (We checked twice a day from tupping onwards, but sometimes she'd be dead by the time you got back with the warmed calcium.)
Not saying this is what happened with yours, just that they can get hypo at any stage, and it kills swiftly.