In 1925, he was awarded the Chess Master title in Braunau. In 1926, he took 3rd in Vienna. In 1936, he tied for 6-7th in Vienna (19th Trebitsch-Turnier; Henryk Friedman won). In 1938, he tied for 6-7th in Bad Harzburg (Vasja Pirc won). In June 1939, he tied for 2nd-4th in Bad Elster (Erich Eliskases won). In July 1939, he took 2nd, behind Eliskases, in Bad Oeynhausen (6th German Championship). In November 1940, he took 4th in Kraków/Krynica/Warsaw (1st General Government chess tournament). In April 1943, he tied for 6-9th in Prague. The event was won by Alexander Alekhine ahead of Paul Keres. In August 1943, he won in Vienna (10th GER-ch). In December 1943, he won in Krynica (the 4th GG-ch).
After World War II, Lokvenc tied for 2nd-3rd in Vienna in 1947. In 1951, he tied for 7-8th in Marienbad (zt). In 1951/52, he tied for 2nd-4th in Vienna. He shared 1st in 1951 and won in 1953 the Austrian Championship. In 1954, he tied for 9-10th in Munich (zt).