It seems so! The verb means "to weigh" figuratively but also literally. And a shekel was, historically, a standard "weight" of a substance used for currency -- such as barley or silver. https://en.wikipedia.org/wiki/Shekel https://en.wiktionary.org/wiki/%D7%A9%D7%A7%D7%9C#Hebrew
Lira לירה was also the name of the currency in Israel from 1952 to 1980.
Bizarrely, when we talk in Hebrew about the British currency, although some of the young and sophisticated would say פאונד, and some would informally say סטרלינג, the newspapers, the banks, and most people say לירה סטרלינג or לירה שטרלינג or write it with the acronym ליש"ט. As you say, there is etymological similarity between "lira" and "pound", but it still strikes me as bizarre.
Sorry I can't edit I'm in the app, colloquial Hebrew cont.: Demonstrative adjectives with the definite article: ‘this’ man ha’ish ha’zeh ‘this’ woman ha’ishah ha’zot ‘that’ man ha’ish ha’hu ‘that’ woman ha’ishah ha’hi ‘these’ boys and girls ha’yeladim v’ha’yladot ha-éleh those boys and girls …ha-hem those girls …ha-hen *You may sometimes hear the more formal ha’élu for the masculine plural.