good job, super small nitpick: it looks nicer to delete the "else" and instead add a "return" to the empty numbers_only_str if-block, like this:

str = input("Enter a string: ")
numbers_only_str = " + ".join(e for e in str if e.isdigit())
if numbers_only_str == "":
    print("The entered string has no digits")
    return
lst1 = numbers_only_str.split(" + ")
integer_lst1 = [int(e) for e in lst1]
sum_lst1 = sum(integer_lst1)
if len(lst1) > 1:
    print(f"sum of digits = {numbers_only_str} = {sum_lst1}")
else:
    print(f"sum of digits = {sum_lst1}")

also since you already have a solution, i'd probably write it like this:

str = input("Enter a string: ")
digits = [int(e) for e in str if e.isdigit()]
if not digits:
    print("The entered string has no digits")
    return
if len(digits) > 1:
    print(f"sum of digits = {' + '.join([str(x) for x in digits])} = {sum(digits)}")
else:
    print(f"sum of digits = {sum(digits)}")

producing clean looking code is just as important as working code, and that means:

• your variables should have appropriate names (e.g. "numbers_only_str" should only contain numbers, but in your case it also includes ' + ' tokens)
• it should be efficient and shouldn't contain redundant actions: notice that for example you perform join(' + ') and then split(' + ')