Yes, the IRS needs to know whether your investment was sold within a year or less after acquiring it (Short Term) or over one year (Long Term), as they are taxed differently.
For tax lots whose term is 'undetermined', use your historical documents to establish the cost basis and date of purchase, since this means that the broker does not have this information.
Determine the acquisition date as accurately as you reasonably can, but the exact date is not critical as long as you correctly determine whether each lot is short-term or long-term.
Then, in TurboTax, you will select the sale category as either "Box B - Short term noncovered" or "Box E - Long term noncovered." You can enter "Various" as the acquisition date as long as you correctly categorize the sale as short-term or long-term.
Here's more info on How Capital Gains are Taxed.
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