Lily, Lydia, or Liliia?
There are several ways to spell Litviak's name in English, depending on which method you prefer to turn the Russian alphabet into English. Names can be translated or transliterated. Translating gives the closest equivalent name; transliterating preserves the original spelling in a different alphabet. The Russian name Михаил is translated as "Michael" and transliterated as "Mikhail;" Иван is translated as "John" and transliterated as "Ivan."
There are several common systems for transliterating Cyrillic. American scholars generally use the modified Library of Congress system. Although it looks somewhat unwieldy in English, it allows one to recreate Cyrillic names and words precisely. Litviak's name in Cyrillic is Лидия Владимировна Литвяк. Her transliterated name in the Library of Congress system is Lidiia Litviak (i for the Russian letter и and ia for the Russian letter я). The usual nickname for her given name of Lidiia was Lida, but Litviak preferred to call herself Liliia (Лилия), which was sometimes shortened to Lilia (Лиля).
Government publications in America favor the United States Board of Geographic Names transliteration system, which is more readable in many people's view, but less precise. This system uses "ya" for the Russian letter я. The United States Board of Geographic Names would transliterate her name as Lidiya/Liliya Litvyak.
One problem in researching Liliia Litviak in English is that you must search for all the variants of English spelling. It's bad enough that Americans use two different accepted transliteration schemes, but many writers seem unaware of either system, and use a hodge-podge of spellings. Thus Litviak is often called "Lily" or "Lydia" (translations rather than transliterations of her first name) and her last name may appear as Litvak or even Litvjak.
For consistency, this site uses Library of Congress spelling for Litviak's names, even when citing works or sites that spell it differently.