Acrylonitrile has been suggested as an alternative membrane-forming material for conditions like those on the surface of Titan, which might allow living cells to develop in liquid methane or ethane solvents. As a fairly small partially-polar molecule, it has a distinct advantage over the long-tailed phospholipids that our biology uses in that it remains liquid at liquid methane temperatures! And supposedly, the liquid nature of cellular membranes is very important for allowing cells to grow and divide, by simply manufacturing more membrane molecules which can slip into the membrane and self-organize.
Unfortunately, acrylonitrile in particular seems (according to this article) to not actually self-assemble into micelles or azotosomes (vesicles formed from nitrogen-containing components) in Titan-like conditions! Based on this earlier article, it seems that acrylonitrile, while getting the most popular press, is not the only potential option for forming low-temperature azotosomes, so all is not necessarily lost... but I have also been thinking that, for example, plants have rigid cell walls in addition to their fluid membranes--and somehow their cells still manage to grow and divide!
So, are fluid membranes really necessary at all? Could very low-temperature life perhaps rely on compartmentalization based on rigid, solid structures formed from larger molecules?
EDIT: Note that, while plant cell walls were an inspiration for this question, they are not actually an answer--plants, fungi, bacteria, and archaea all have cell walls, so clearly it's a useful structure, but they all have different, convergently-evolved, cell walls, and they all have very complex cell walls with a lot of cellular machinery to manage their maintenance and growth. A good answer to this question would provide a plausible explanation for how a simple rigid compartment, analogous to a cell membrane, could arise during abiogenesis--or explain why such a thing is not plausible after all.