I don't think you necessarily need Li-ion for that - in my experience lead acid works well enough in the domestic case, is a lot cheaper and probably safer (although hydrogen venting is perhaps an issue).

I built a little mixed DC (lighting) + AC (1kW inverter) system out in the garden (far enough from the flat that running a cable would be a nightmare of planning permissions & digging trenches).

Since it's for intermittent use the panel is tiny (50W Kyocera) compared to the battery (110 Ah 'leisure') & inverter (1kW true sine), and it works just fine even here at 53 deg latitude. It would scale up for the entire house quite well, were it not for the fact that it's a four-in-a-block with a communal roof, and 1/2 loft space unusable due to loft conversion.