You can use EOMONTH
with a bit of extra logic:
LastDay =
VAR CurrDate = MAX(Table1[Date])
RETURN CALCULATE(MAX(Table1[Date]),
FILTER(ALL(Table1),
Table1[Date] > EOMONTH(CurrDate, -1) &&
Table1[Date] <= EOMONTH(CurrDate, 0)))
This takes the max of the dates you have that occur between the end of the previous month and the end of the current month.
Once you have this measure, you can use it to calculate the sum of Value
:
Last Date Sum = CALCULATE(SUM(Table01[Value]),
FILTER(Table01, Table01[Date] = [LastDay]))