There are too many variables to make a simple statement. Lead-acid is a lot cheaper and we know how to recycle it. We also have a long proven history of lead acid lasting for decades in ideal conditions (which a house battery is more likely to hit than in a car).

However lead-acid does not like deep discharge so to get max life you will be using much less than the full discharge cycle 80%-100%, and so the lifecycle costs are very different. In some cases lead-acid can be more cost effective if you manage it well, but I would expect lithium to be cheaper for the typical case.

That is lead acid means your real goal is a cheap home backup, which you have to ride out multi-day power outages, and as a secondary you will sell some power to the grid, but you are not trying to make money doing this. By contrast I would expect lithium to make sense if your primary goal is to make money (or at least pay for your home backup system that can ride out a couple hours of outage but not days). The storage to ride out days could work now, but long term as your neighbors buy the system eventually there isn't the need for that much storage and someone gets limited.