As always, it would help if expected outputs were provided. All we can go on right now is your hand-wavy description. It sounds like you want to rationalize a list of numeric data. The function to do that is Rationalize. DanielL has already demonstrated how to use it. In your new example, you could again just do

Rationalize[gensSG141ITA1]

If that does not produce the desired output, then you'll need to explain the difference between what Rationalize gives you and what you want.

If I allow myself to speculate, then based on the name you gave your function, RationalizeitIfNot, it sounds like you might be thinking that if a number is already rational then you don't want to do anything to it. But applying Rationalize to a number that's already rational is safe. So there's no reason to apply it conditionally. But that's just speculation. You should really provide expected outputs.

What I mean is like the following:

In[5]:= RationalizeitIfNot[l_list] := l

In[4]:= gensSG141ITA1 = {
    {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
    {{-1, 0, 0, 1/2}, {0, -1, 0, 1/2}, {0, 0, 1, 0.68}, {0, 0, 0, 
     1}},
    {{0, -1, 0, 0}, {1, 0, 0, 0.54}, {0, 0, 1, 1/4}, {0, 0, 0, 1}},
    {{-1, 0, 0, 1/2}, {0,  1, 0,  0}, {0,  0,  -1, 0.47}, {0, 0, 0, 
     1}},
    {{-1, 0, 0, 0}, {0, -1, 0, 1/2}, {0, 0, -1, 1/4}, {0, 0, 0, 1}},
    {{1, 0, 0, 1/2}, {0, 1, 0, 1/2}, {0, 0, 1, 1/2}, {0, 0, 0, 1}}
   }; 

In[6]:= RationalizeitIfNot[gensSG141ITA1]

Out[6]= RationalizeitIfNot[{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 
    0}, {0, 0, 0, 1}}, {{-1, 0, 0, 1/2}, {0, -1, 0, 1/2}, {0, 0, 1, 
    0.68}, {0, 0, 0, 1}}, {{0, -1, 0, 0}, {1, 0, 0, 0.54}, {0, 0, 1, 
    1/4}, {0, 0, 0, 1}}, {{-1, 0, 0, 1/2}, {0, 1, 0, 0}, {0, 0, -1, 
    0.47}, {0, 0, 0, 1}}, {{-1, 0, 0, 0}, {0, -1, 0, 1/2}, {0, 0, -1, 
    1/4}, {0, 0, 0, 1}}, {{1, 0, 0, 1/2}, {0, 1, 0, 1/2}, {0, 0, 1, 1/
    2}, {0, 0, 0, 1}}}]

This is just an example. In my actual situation, I need to determine the data in the array list provided to the user-defined function in real time, and then do the corresponding processing described here.