Adding sublists elements based on indexing by condition in python

Here's an itertools based approach:

from operator import itemgetter
from itertools import groupby, islice

l = sorted(a+b)
[[k] + [sum(i) for i in islice(zip(*v),1,None)] for k,v in groupby(l, key=itemgetter(0))]
# [['a', 1, 2, 1, 3], ['b', 2, 6, 8, 6], ['c', 2, 6, 8, 6]]

You can define a function like this one:

def add_elements(a, b):
    b_dict = {i[0]: i[1:] for i in b}
    default = [0 for _ in a][:-1]
    return [i[:1] + [sum(x) for x in zip(i[1:], b_dict.get(i[0], default))] for i in a]

And call it with your lists as arguments:

add_elements(a, b)
#[['a', 1, 2, 1, 3], ['b', 2, 6, 8, 6], ['c', 2, 6, 8, 6]]

see @zipa's answer for a more Pythonic (efficient, short, readable, overall better) solution using dictionaries.

I will try to answer using the original structure of your own code:

from operator import add

a=[['a',1,2,1,3],['b',1,3,4,3],['c',1,3,4,3]]
b=[['b',1,3,4,3],['c',1,3,4,3]]

res_list1=[]
for a1 in a:
    found_match = False
    for b1 in b:
        if a1[0]==b1[0]:
            found_match = True
            res_list = [map(add, a1[1:], b1[1:])]
            res = [[a1[0],i,j,k,l] for i,j,k,l in res_list]
            res_list1.append(res[0])
    if not found_match:
        res_list = a1
        res_list1.append(res_list)

print(res_list1)

The problem you had is always appending to res_list1, every iteration of the inner loop (so for every (a1,b1) pair). what I did to solve this is "remember" (that is - keep in a boolean variable) whether we found a match for a1 in b, and only if not - add the original list to the result