TypeError: 'int' object is not subscriptable

The error is exactly what it says it is; you're trying to take sumall[0] when sumall is an int and that doesn't make any sense. What do you believe sumall should be?

Just to be clear, all the answers so far are correct, but the reasoning behind them is not explained very well.

The sumall variable is not yet a string. Parentheticals will not convert to a string (e.g. summ = (int(birthday[0])+int(birthday[1])) still returns an integer. It looks like you most likely intended to type str((int(sumall[0])+int(sumall[1]))), but forgot to. The reason the str() function fixes everything is because it converts anything in it compatible to a string.

If you want to sum the digit of a number, one way to do it is using sum() + a generator expression:

sum(int(i) for i in str(155))

I modified a little your code using sum(), maybe you want to take a look at it:

birthday = raw_input("When is your birthday(mm/dd/yyyy)? ")
summ = sum(int(i) for i in birthday[0:2])
sumd = sum(int(i) for i in birthday[3:5])
sumy = sum(int(i) for i in birthday[6:10])
sumall = summ + sumd + sumy
print "The sum of your numbers is", sumall
sumln = sum(int(c) for c in str(sumall)))
print "Your lucky number is", sumln