There's a number of "immortal" human cell lines dating back to as far as the 1950s (you may have heard of Henrietta Lacks? [1] and the immortal HeLa cell line).

Today there are several immortalized neuron cell lines used in research to model neuronal function, like HeLa but of neuron type obviously, that are also typically derived from tumours (e.g., SH-SY5Y, PC12) or immortalized via genetic modification (e.g., v-myc) like CTX0E03 [2] which was designed to allow for continuous growth in the presence of particular reagents.

1. https://en.wikipedia.org/wiki/Henrietta_Lacks

2. https://www.prnewswire.com/news-releases/reneuron-announces-...