Lushta was born on 22 January 1916 in Kosovska Mitrovica, Kingdom of Serbia (present day Mitrovica, Kosovo). It was in his hometown that he would begin to play football with the local club Rudari Trepča, where he quickly established himself as one of the most effective strikers the city and even region had ever seen. After spendin with Rudari Trepča Lushta two years left Kosovo in 1934 and went to Albania to join the Harry Fultz Technical School in Tirana and in that time he joined two time Albanian champions SK Tirana. His career with Tirana immediately took off, winning the league title in his first season in Albania, before going on to win it a total of four times between 1934 and 1939, as well as the inaugural King's Cup in 1939. He left Albania and SK Tirana in 1939 following the Italian occupation of Albania to join Bari in Italy, where he scored 3 times in 16 games during his first season in Italy. His performances with Bari attracted the interest of Juventus who he joined in 1940 after just one year with Bari. In his first season with Juventus he scored 9 times in 26 games before netting 15 goals the following season to be named the highest scoring foreigner of the 1941–42 Serie A.