There are dozens of internet sites that make reference to a match between Max Lange and Wilhelm Steinitz in Vienna in 1860, although none that I have found offer any details concerning this match. There were three games, all won by Steinitz. Black's play does not reflect the level of skill that might be expected from the editor of Schachzeitung der Berliner Schachgesellschaft, a chess newsletter. The publication was founded in 1846 and became Deutsche Schachzeitung in 1872. It continued publication until 1988. Lange was the editor 1858-1864. In 1860, Max Lange published Paul Morphy: A Sketch from the Chess World, translated into English by Ernest Falkbeer. Lange was an active and knowledgeable chess player in 1860. In 1862, he won the West German Championship.
Did Lange visit Vienna in 1860 and get trounced by Steinitz? It is possible. However, it is easier to believe that Steinitz won these lopsided games against a local Vienna player with the last name of Lang (without the e). Dozens of internet sites have Lang with no first name, but also no details.
Whoever played Black had his mistakes trounced by a sacrificial attack against the king that merits attention by improving chess players. Steinitz understood that material could be given up if it led to the execution of his opponent's king.
Steinitz,William -- Lange,Max or Lang [C44]
1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Qe7 5.0–0 Ne5 6.Nxe5 Qxe5 7.c3 c5 8.f4 Qf6 9.e5 Qb6 10.Kh1 Be7 11.f5 d5 12.Bxd5 Nh6 13.f6 Bf8 14.Bxh6 gxh6
Black has made several positional errors already in this game. Now the tactics begin. This position appears on the demonstration board in youth chess clubs this week. One young player won a chess pencil for suggesting the correct move (and later revealed that he suggested it because he thought it was "stupid"--the "stupid move is often the correct one in these problems").
White to move
15...Kd8 was a better choice for Black, although White still has a considerable advantage after 16.cxd4 Qxb2 17.Nd2
16...Kg8 also loses 17.Rf3 Qe6 18.Rg3+ Bg7 19.Qxh6 Kf7 20.Qxg7+ Ke8 21.Qxh8+ Kd7+-
17...Be7 was possible, leading to 18.Qxh8 Qd8 19.Qxh7 Bf8 20.cxd4+-
18...Qxb2 offers more stubborn defense 19.Qd8+ Kc6 20.d5+ Kb5 21.Nc3+ Ka6 22.Rab1 Qxc3 23.Rf3+-
White to move
19.Nc3+!! Kc4 20.d5 Rxe8
20...Kd4 or 20...Qxb2 hold off checkmate longer.
21.Rf4+ Kd3 22.Rd1+ Kc2 23.Rf2# 1–0