Rahamim was born September 20, 1909 in Benghazi, Libya to Nina and Elimelech Labi. As a youth, he began learning to be a tailor, beginning his career in his hometown. During World War II, he was a tailor for the British Army. His work led him to a transit camp in Egypt in 1942. There he found Hadassah Nimni, whom he had first met in Benghazi, and they married. The young couple made aliyah legally, as they had British citizenship. They settled in the Shaarayim neighborhood in Rehovot, where Rahamim established a business and continued to work as a tailor. Among his clients were Egged bus drivers and a number of senior military officers.

One day a Lehi member came to his home to ask him to hide some important material for the underground. Rahamim was happy to do it. When the underground operative returned and asked him for the material, Rahamim said to him: “Find it yourself.” The operative searched thoroughly, both in the shop and at his home, but could not find it. He told Rahamim: “You are hereby accepted to the underground.” Rahamim was overjoyed and immediately became one of Lehi’s most active members. He was suspected, arrested and sat in Jaffa’s Qishle Prison. The second time, he was sent to Acre Prison, but he was soon released. His house was a meeting place for Lehi members and a hiding place for their arms. His wife Hadassah (“Delilah”) served in Lehi as well.

After the War of Independence, Rahamim and Hadassah bought a home in Shikun HaVatikim, and spent the rest of their lives there.

The Lavi family had six children and numerous grandchildren. Rahamim died of a severe illness in May 20, 1993 and he was buried in the old cemetery in the Marmorek neighborhood of Rehovot, alongside his wife.