A "store of value" when talking about the properties of a useful currency implies that the value is largely stable so that it can be "stored" over the medium- and long-term. So that's actually the property BTC is worst at due of its volatility. Actually, no, 4 transactions per second globally means "medium of exchange" is the property of money BTC is worse at.
Your point that BTC was supposed to be a currency and has turned into a speculative asset is true though, and BTC proponents often dislike it when someone points that out. LN is just an attempt to make BTC better as a "medium of exchange" which is fine, but it still doesn't address the fact that BTC is a terrible store of value, it just reduces the volatility of the transaction fee (in theory).