I understand
a = max(set(lst), key=lst.count)
will derive most common element in a list
but how do you derive most common element
There are many ways, but I wanted to let you know that there are some nice tools for that kind of things in the standard modules, e.g. collections.Counter:
In [1]: lst = [['1','2','3','4'],['1','1','1','1'],['1','2','3','4']]
In [2]: from collections import Counter
In [3]: from operator import itemgetter
In [4]: max((Counter(l).most_common(1)[0] for l in lst), key=itemgetter(1))[0]
Out[4]: '1'
Or, you could (kinda) employ your current solution for each of the sublists:
In [5]: max(((max(set(l), key=l.count), l) for l in lst),
...: key=lambda x: x[1].count(x[0]))[0]
Out[5]: '1'