The result of input in Python 3 is always a string. The sum function is then trying to add each item of the list together, starting with 0, so it attempts to to this:
0 + your_list[0]
But, the first item of your list is a string, and you can't add an integer to a string.
To get around this, convert the input to an integer first by using the int function:
print('Enter a series of integers. Hit enter to quit')
lst1=[]
lst2=[]
while True:
get1=input('Enter: ')
if get1=='':
break
lst1.append(int(get1))
while True:
get2=input('Enter: ')
if get2=='':
break
lst2.append(int(get2))
if sum(lst1)==sum(lst2):
print('The two lists add up the same')
else:
print('The two lists do not add up')
Note that I've moved the if statements before the integer conversion, because otherwise entering '' will cause an exception to be thrown as an empty string isn't a valid integer.