On his website (now only available via Internet Archive), he claims to have used the same Herodotus machine to raise and place the lintel as he did for raising the initial supports:

https://web.archive.org/web/20161107075626/http://www.thefor...

I imagine once he'd gotten the supports placed, he could just raise the lintel between them with the machine, perpendicular to its final resting position, then rotate it into place.

To get an initial fulcrum under a stone, it looks like he built a wrench-shaped wood frame, essentially attaching a long lever handle to the stone. One can be seen in the second picture on this page:

https://web.archive.org/web/20161206062032/http://www.thefor...