Probably maybe, maybe not?

It depends where you out the boundaries of life. The unfortunate answer is that this may not be a scientific question, or at least not a question the scientific method can answer because we just won't be able to get evidence from the period if time where we could answer this question.

But a few things to think about along the way. There are two big considerations when it comes to the evolution of cells, and what purpose they serve. The first is an issue around concentration and the second is on gradients. Firstly, one of the biggest issues you have around creating the conditions for the evolution of life is concentrating enough material, in an area to have meaningful concentration density for life processes to occur. This is one of the main arguments against life starting in the oceans. You would need massive concentrations of basic chemical ingredients to get any kind of meaningful interactions because of this. The second point is around gradients. Almost all life processes are modulated through some kind of a barrier, usually a cell membrane, where a bunch of stuff is on one side of the barrier, and by either moving through or interacting across the barrier, "work" happens, that work being the stuff of life. You need a barrier to set up some kind of a concentration gradient separating compound A from compound B.

Cells as phospholipid bilayers, accomplish both of these things. It creates an opportunity to keep things concentrated and it also gives an opportunity to create gradients.

Life is a steady process held out of thermodynamic equilibrium with its environment. There are many such systems that are not living systems that have this same property. It's in these systems that complexity can arise.

It could be that in the proto biological phase of earth, there might have been a system where cell like structures could have emerged through a simple chemical, thermodynamic process. In such a system, so long as there is material and energetic flow, it might be that these kinds of concentration gradients naturally arise.

Now, that's more on the speculative evolutionary biology side.

On the "what evidence we do have" side, among bacteria and phages, we see a far more significant diversity in cell membrane or cell wall type materials than we see among eukaryotic life. If you put your chalk line down at eukaryotes, almost assuredly there was one common ancestor. This is just accepted biological theory at this point.

However, there is far more diversity when you get into bacteria, archea, and phages when it comes to the molecular construction of how they keep the inside bits from the outside bits separated. But it's not clear if these point to a LUCA or not.

To summarize. It's pretty hard to imagine life without cells because it's almost impossible to create the kinds of concentration of materials necessary to do so, and we basically define life as the stuff which happens across one a gradient, which we don't see happening outside of the concept of cells. If might we'll be that cells evolved first, through some arbitrary natural process, and life processes emerged across a simple system where some chemistry could become concentrated and barriers existed to create gradients.We have some evidence that there are a wide range of materials used for cell membrane, however, this doesn't them out a LUCA.