That's the key word: lost. Nothing's been lost - neither Eli Lilly nor their shareholders have lost any money (unless they sold their stock, at which point they aren't shareholders). The price of their stock dipped, and is rising back up.
At worst, Eli Lilly would have had slightly higher interest rates on their next round of debt funding.
You're assuming that brand value has no financial value. Forget the stock price, this probably impacted EliLilly's brand in a way that will cost a bunch of money to "fix". If it sparks renewed calls for regulatory action on insulin prices, it could cost them quite a bit more than just brand value as well - either in lobbying, political "contributions", or profits. But that's speculation for now.
The people selling based off of tweetstorms or breaking news are not mom and pop investors saving for retirement. They’re day traders trying to squeeze profit out of fluctuations.
Timing the market is impossible, besides selling now would be a good thing if they bought the stock at any point more than 1 month ago. Go look at the stock chart.
The stock has recovered 60% of the maybe-Twitter-related losses. The stock lost 5% of its value on November 11th, and recovered 60% of that to date which means the maybe-Twitter-related drop in value is 40% of 5%, or 2%.
However, Friday also saw a broad drop in pharma stocks. If I'm quite generous I'd say 50% of that 2% can be attributed to the Twitter tomfoolery.
At worst, Eli Lilly would have had slightly higher interest rates on their next round of debt funding.