In the league, he ended the season on 30 appearances as Brøndby finished in third place. The 2015–16 season saw less playing time for Ørnskov, as Christian Nørgaard emerged as a starter at his position on defensive midfield. He made 32 total appearances, most of them as a substitute. Ørnskov departed Brøndby as his contract with the club expired in June 2016. On 20 June 2016, Ørnskov signed a two-year contract with Lyngby BK. He scored his first goal for Lyngby in his first return to Brøndby Stadion, securing a 2–0 win over his old club. That season he made 38 appearances in which he scored one goal as Lyngby surprisingly ended in third place and qualified for the Europa League. The following season, Lyngby were relegated from the Danish Superliga after losing in decisive play-off matches to Vendsyssel FF after a terrible season where the club was on the verge of economic collapse. Ørnskov ended the 2017–18 season with 42 appearances and two goals. Ørnskov signed a one-year contract extension on 4 July 2018, keeping him a part of "De Kongeblå" at least until 2019. Later that month, coach Mark Strudal appointed Ørnskov as new club captain, replacing Mathias Tauber who had captained the side for more than six years. Tauber's contract with the club was terminated the same day. Despite the rocky start to the season, Ørnskov captained Lyngby to promotion to the Danish Superliga after only one season in the second tier. Following the promotion, Ørnskov signed another one-year contract extension on 4 June 2019.