Assuming Lost_Sales is recorded per date and location only, you can use SUM(Omits) OVER (Date,Location) to calculate the sum of omits for each key combination.

For example

Select 
    1.00*lost_sales*omits/SUM(Omits) OVER (Date,Location) As New_Lost_Sales
FROM
...

You may have to adjust the query in case SUM(Omits) can be null or 0 , eg SUM(ISNULL(Omits,0)) .

Without the actual tables and sample data one can only make guesses. What happens for example if SUM(Omits) is 0 but Lost_Sales isn't? Are fractional lost sales acceptable?

Let's say you want to retain Lost_Sales if SUM(INSULL(Omits,0)) is 0. To avoid repeating the SUM clause, you can use a CTE to calculate it once and use it in an IIF clause:

WITH omits as (
    Select 
        ...,
        SUM(Omits) OVER (Date,Location) as TotalOmits
    FROM
    ...
)
select *,
    IIF(TotalOmits=0,
        Lost_Sales,
        1.00*lost_sales*omits/TotalOmits) as New_Lost_Sales
FROM omits

do you want something like this

WITH CTE AS (
  SELECT
    Date,
    Location,
    Product,
    CompanyID,
    SUM(Omits) AS TotalOmits
  FROM YourTableName 
  GROUP BY Date, Location, Product, CompanyID
)

SELECT
  t.Date,
  t.Location,
  t.Product,
  t.CompanyID,
  t.Omits,
  t.Lost_Sales,
  (t.Omits * 1.0 / c.TotalOmits) * t.Lost_Sales AS New_Lost_Sales
FROM YourTableName t 
JOIN CTE c
  ON t.Date = c.Date
  AND t.Location = c.Location
  AND t.Product = c.Product
  AND t.CompanyID = c.CompanyID;