He was born into the family of František Liška Sr. (1850–1905), a builder active in Skuteč and, from 1883, also in Chotěboř while he was working on a commission in Holba near Hanušovice. Like his brothers Otakar (1876–1912) and Vladimír (1885–1934), it is probable he studied civil engineering at the Czech Technical University in Prague. He gained his first professional experience as a construction manager in his father’s firm in Chotěboř. In 1908, he obtained a builder’s licence in Chotěboř and took over the family business following his father’s death. Together with his brother Otakar, he subsequently founded the construction company Otakar and František Liška in Německý (Havlíčkův) Brod. After his brother’s premature death in 1912, he acquired a builder’s licence in Německý Brod and took over the Brod-based company, which he operated alongside a steam sawmill and a ring kiln brickworks. These enterprises developed successfully, and he therefore transferred the Chotěboř firm to his brother Vladimír, who was also a civil engineer. During the first two decades of the 20th century, his company was among the leading construction firms in Brod. During its existence, it completed numerous projects for the town and for private clients, including the Postal and Telegraph Office (1910), the District House (1911), and the Farmers’ House (1925).

František Liška did not limit himself to construction contracts alone; if a client showed interest, he also offered architectural services. In his early years, these were executed in the then-fashionable historicist style, continuing the tradition of his father’s work. His interest in contemporary developments is evident, for example, in the 1920s, when he embraced new technologies and trends such as reinforced concrete structures, which were especially popular among functionalist architects. In Německý Brod, he applied this technique in 1927 when collaborating on the architectural design of the congregational building for the Czechoslovak Church.

He also established himself as a designer and builder of family houses and villas in the town, including, for example, the Prokop Villa, Strážná 1432 (1911); his own villa, Jihlavská 318 (1920); and the Knap Villa, Nad Tratí 537 (1934).