After beginning his professional career with Midtjylland, he played in France for Guingamp, in Germany for Mainz 05, and in England for Huddersfield Town and Everton.

Lössl made his senior international debut for Denmark in March 2016 and was part of their squad at the 2018 FIFA World Cup and 2020 UEFA Euro.

[8] Following Huddersfield Town's relegation from the Premier League in 2019, Lössl joined fellow English club Everton on a free transfer on 1 July 2019.

[12] There, he took over after former starter Jesper Hansen,[13] but eventually saw himself benched in favour of Elías Rafn Ólafsson after returning from injury under new head coach Bo Henriksen during the 2021–22 season.

[17][18] He then regained the starting goalkeeper position at Midtjylland following the appointment of new head coach Albert Capellas in late August 2022.

[25] On 29 March 2016, Lössl made his Denmark debut as a half-time substitute for Kasper Schmeichel in a 1–0 friendly loss to Scotland, keeping a clean sheet in his 45 minutes.