Depending upon your view of lightning chess, the Jerome Gambit may a very good - or very bad - fit for such hectic play.
In the following game, Black's quick-play strategy is to move his pieces, not his pawns. This falls right into White's hands, however.
KingDeath - FoxTerrier
lightning, FICS, 2013
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.0-0 Nf6 5.Bxf7+
Transposing to a "modern" variation of the Jerome Gambit - 4.Bxf7+ Kxf7 5.0-0 Nf6
5...Kxf7 6.Nxe5+ Nxe5 7.d4 Bxd4 8.Qxd4 Nc6 9.Qc4+ Kf8
10.Bg5 Qe7 11.Nc3 Qe5 12.f4 Qe8 13.e5 Ng8
14.Nd5 Qf7 15.Qc5+
Black forfeited on time.
A good exercise is to see how many times a pawn move would have suited Black better than the move he chose. (My guess is at least on moves 9, 10, 11, 13 and 15.)
