So SEELE was helpless without the Lance of Longinus in beginning the Third Impact after Rei and Eva-00 hurled it into the moon?
No. Keel Lorenz makes it clear that when the Lance was thought to be lost that they still had another key to our evolutionary jumpstart. All SEELE had to do was use an Angel like I was planning to use Rei or the EVA-01 with its new S2 Drive instead of Lilith herself (but with the Unit-01 nobody was sure if it would truly work). It is obvious that he originally wished to keep some control of the Impact by using the Lance, Lilith, and Adam. But when the Lance was gone he just wanted to get it over with. He must have decided that eternal sleep was at least a consolation prize for his long quest even though he could not become a god by controlling the Impact and merging with first Adam and then Lilith himself (the forbidden fusion that I attempted to do with Rei). SEELE had been working on an artificial Lance of Longinus, but it is assumed that unlike their fully functional S2 Drives, the Lances were never fully completed (although the EVAs 05-13 never got the chance to test the replicas t