He was born on 22 January 1916 in Sanok. After passing his matriculation exams in 1936 at the Stanisław Staszic State Industrial School in Kraków, he took a glider course in Bezmiechowa Górna, becoming an "A" category glider pilot. In 1937, he began his military service at the Communications Officer Cadet School in Zegrze and was then sent to the Air Force Reserve Officer Cadet School in Dęblin. After completing a basic pilot course, he was assigned to the 6th Aviation Regiment in Lwów.

On 21 July 1939, he was called up for reservist exercises to the Training Escadrille of the 6th Aviation Regiment. After completing his training, he was not released home but, shortly before the outbreak of war, was assigned to the 66th Observation Escadrille. When the war broke out, he was stationed at the airport in Tarnopol. After the Soviet Union attacked Poland, he was sent to Kraków and then to Sanok, where he took up a job in an oil mine in nearby Grabownica Starzeńska.

In May 1940, he joined a group of 10 people who crossed the border into Hungary in the Baligród area without being detected. Then, via Yugoslavia, Greece and Turkey, he arrived in Haifa to join the Independent Carpathian Rifle Brigade on 19 August 1940. He arrived in England in October 1940, first at an aviation centre in Blackpool and then in Newton, where he received training at No. 16 (Polish) Service Flying Training School. During the course, he was promoted to the rank of second lieutenant on 1 February 1942.

On 20 October 1942, he was assigned to No. 304 (Land of Silesia) Polish Bomber Squadron, stationed at that time at Dale, Wales, and under the orders of the RAF Coastal Command. He made his first flight on 28 October 1942. He was flying in combat on Vickers Wellington aircraft. His tasks included patrolling, photographing and bombing enemy naval vessels, including German submarines. He also was engaged in the bombing of the port of Bordeaux. By February 1943, he had flown in combat sixteen times.

From 10 September 1943, now with a new crew, he made a further 34 flights and combat assignments, mainly over the Atlantic Ocean and the Bay of Biscay. After completing a total of 50 flights (the last on 21/22 June 1944), he was sent on an instructor course at the 16 SFTS pilot school. After completing it, he trained pilots as an instructor on Airspeed Oxford aircraft.

For his bravery in combat, he was awarded the Cross of Valour and the Silver Cross of the Virtuti Militari War Order. After the end of the war, he rejoined the No. 304 Squadron, which then became a transport unit, and later – until the unit's disbandment in December 1946 – he served in No. 301 (Land of Pomerania) Polish Bomber Squadron.

After leaving the service, he stayed in the UK. He returned to Poland in 1988. By order of the President of the Republic of Poland Andrzej Duda, he was appointed to the rank of brigadier general on 28 September 2016. Ludwik Krempa was presented with his promotion to general by the President in person on 25 November 2016 in Kraków.

He died on 3 January 2017 in Kraków. He rests in his parents' tomb at the Central Cemetery in Sanok.