L.Kosakivskyi was born on January 21, 1950 in the village of Chernivtsi of Mogyliv-Podolskyi district in Vinnitsa region. He is a Ukrainian. Mr. Kosakivskyi's profession is a radio physicist. 

His  spouse,  Iryna  Kosakivska, is a Head of Department of Phytohormonology of the Institute of Botany of the National Academy of Sciences of Ukraine. She is professor, doctor of biological sciences, specializing in the physiology of stress and adaptation of plants, author of over 320 scientific publications, including six monographs, two of which are sole-authored. 

They have an adult son, Sergei. In 1995 he graduated with honors from the Cybernetics Department of Kyiv National Taras Shevchenko University. He received a doctorate of philosophy (PhD) in Applied Mathematics at the University of Arizona (USA). Now he is full Professor of Biology, Institute for Genomics and Evolutionary Medicine, Director, Center for Viral Evolution, Temple University, Philadelphia, USA. He is a Highly Cited researcher (2014 – 2017, 2023) by Highly Cited Researchers.

 After graduating from T.G.Shevchenko University in Kyiv, Mr. Kosakivskyi served in the army in air defence troops since 1973 up to 1975. He worked at the “Arsenal” plant for 5 years. In November 1988 Mr. Kosakivskyi was one of the first candidates who won the democratic elections on alternative basis and became the First Secretary of the Pechersk District Committee of the Communist Party in Kyiv. In 1990 he was elected the deputy of Pechersk District Council of People's Deputies, a Deputy of the Kyiv City Council. Since January 1991 — Head of the Pechersk District Council of People's Deputies and its Executive Committee. Starting with April 1992 Mr. Kosakivskyi was the Representative of the President of Ukraine in the Pechersk District and starting with April 1993 he was the Representative of the President of Ukraine in the city of Kyiv.

 On July 10, 1994, for the first time in the history of the city, Mr. Kosakivskyi was elected the Head of the Kyiv City Council as the result of the free democratic elections with the direct voting of all citizens of Kyiv.

 Starting with the very first days after his election, he began to implement persistently and consistently his programme, supported by the citizens of Kyiv, into life. Mr. Kosakivskyi aimed to be the mayor for all inhabitants, to serve them, but not the certain political parties, to defend the interests of the city in everything, as he had promised.

 It was during this period, when Mr. Kosakivskyi had real levers of power, that the course for the support and development of industry and science in Kyiv was chosen. The construction works were preserved and resumed. During the period of 1994 – 1995 1.6 times more residential houses and 4 times more schools and kindergartens were built as compared to the period of 1996 – 1997 (when Mr. L.Kosakivskyi was dismissed from the power). It was decided to start the reconstruction of the houses built in the 60-ties. The situation with the city traffic was improved. A great number of new buses, trolley-buses, trams was purchased. The programme of metro lines development up to the year of 2010 was approved and its realisation was started. For the first time the organisation of the summer health improvement for children financed by the city budget was initiated. Great attention was paid to the social assistance programmes and work for the benefit of veterans. The financial situation of the city was stable. Kyiv had the best results in Ukraine according to the majority of economic characteristics.

 Those years were marked by considerable changes in the spiritual sphere. Kyiv got back his historic coat of arms and flag. The revival of Kyiv trade fairs, historical and cultural monuments was started. The monument to the Great Princess Olga was restored, the decision about the beginning of the restoration of the Church of the Virgin Mary of Pirogoshchy, Mikhailivskyi and Assumption Cathedrals was approved, the names of famous S.Lyfar and V.Gorovits were returned to their native city. “Spivoche Pole” ( the Field for Singing) one of the favorite rest places for Kyiv’s citizens, was build.

 But they did not let L.Kosakivskyi implement everything he planned. The central authorities were worried about the growing independence of the city and its leaders, about the reluctance of the Head of the Kyiv City Council to transfer a number of objects from the city property into the state property, to allot certain plots of land for construction works, to provide flats for ever increasing number of members of the state government and especially about the desire of L.Kosakivskyi to turn Kyiv into self-governed city. And most of all the authorities were concerned with the disapproval of the Head of the Kyiv City Council regarding the plans for the reconstruction of the Palace of Culture “Ukraine” and with his suggestion to reallocate this money for metro construction. Besides, he refused to provide a land plot for the Administration of the President, so that a multistoried "President-Hotel" can be built in the park near Mariinsky palace, and he opposed the construction of the house for the elite in Desyatinna street, number 10.

 The central authorities took advantage of the Constitutional Agreement, according to which, starting with July 1995 Mr. Kosakivskyi simultaneously occupied the position of the Head of the Kyiv City Council and the position of the Head of the City State Administration, and they dismissed him from the position of the Head of the City State Administration during his illness in July 1996. But having no opportunity to dismiss Mr. Kosakivskyi from his position of the Head of the Kyiv City Council, to which he was elected by the citizens of Kyiv, the authorities made attempts to intimidate and to block his activity. The Kyiv City Council was artificially split up, it was prevented from gathering for the legitimate meetings. As the result of it, the City Administration illegally usurped the powers of the Kyiv City Council as to the management of land, property, finances. In fact, the direct presidential ruling was introduced in Kyiv.

 Feeling their failure to force Mr. L.Kosakivskyi on his knees, the central authorities tried to dismiss him again from his position in June 1997, taking advantage of the new law on local self-government, according to which Mr. L.Kosakivskyi, elected by the citizens of Kyiv, received a new status of the City Head. Despite the fact, that the Supreme Rada of Ukraine, the Council of Europe supported Mr. Kosakivskyi, and the Starokyivskyi district court and Supreme Court completely restored his rights and cancelled the illegal decision of the deputies, the executive power continued to block the work of the city mayor and to keep police at the doors of his office.

 But Mr. L.Kosakivskyi did not surrender, did not betray his electors, he worked, continued his fight against the high-handedness of the officials for the return of the power to the hands of the citizens of Kyiv, he promoted the protection of the self-government in Kyiv in the Law on local self-government, in the Law on the capital city, he attracted the attention of the Council of Europe to the problems of local democracy in the capital.

 On 30 March 1998, against the oppositions of officials, Mr. L.Kosakivskyi was elected a People's Deputy of Ukraine in the constituency 223 in Kyiv. He was a People's Deputy of Ukraine (MP) from 1998 until 2002. He was a member of the Committee on Budget.

 Member of the Delegation of Ukraine in the Congress of Local and Regional Authorities of the Council of Europe from 1996 to 1998.

 Member of the Permanent Delegation of The Verkhovna Rada of Ukraine in The Council of Europe Parliamentary Assembly from 1998 to 2002.