How to lower all the elements in a pandas dataframe?

Either

df.applymap(str.lower)
Out: 
   X  Y  Z
0  a  b  d
1  c  e  c

Or

df.apply(lambda col: col.str.lower())
Out: 
   X  Y  Z
0  a  b  d
1  c  e  c

The first one is faster and it looks nicer but the second one can handle NaNs.