I am looking for a clause that has a meaning of "lessen load."
Here is the sentence that I was writing:
As a good son, lessening father's load is a natural duty.
There may not be a single word that does exactly what you want, but consider alternative ways of phrasing:
As a good son, lightening the father's burdens is a natural duty.
As a good son, it is a natural duty to try to lighten the father's burdens.
I chose "burden" instead of "load" because "burden" conveys both the weight and the responsibility. I chose the plural "burdens" because there could be more than one. I chose "lighten" because it matches the concept of burdens being heavy. You may want to consider adding "try to" as I did in my second example because presumably you don't want to consider it a duty when it is impossible.
Finally, I added "the" before "father" because it is referring to a definite entity. Depending on your context, "my father" or "one's father" may be more appropriate.