[2] Her father is Štefan Luby, a prominent physicist and a former president of the Slovak Academy of Sciences (1995–2009).

Following the example of her father, she studied biophysics at the Faculty of Mathematics, Physics and Informatics of the Comenius University, graduating in 1991.

[3] In 2010, she rejoined the Slovak Academy of Sciences and taught statistics at the University of Economics in Bratislava.

[4] Lubyová became Minister of Education on 11 September 2017 as a nominee of the Slovak National Party, replacing Peter Plavčan, who was forced to resign after corruption allegations related to distributions of European science funding.

Lubyová defended the party's chairman, Andrej Danko, accused of plagiarism in his Master's thesis, claiming that it is not right to harass people 20 years after their graduation "because of some missing quotations".