A big storm which uproots the strongest and the biggest trees, doesn't harm the small grass grown on the ground! (If a big storm can uproot the huge tree then why can't it uproot a small grass from the ground?!)
Like wise the strong people who have good qualities will not trouble the poor who have less might as compared to themselves. The other meaning of this subhAshita can be taken as there should be 'dvandva' (Fight) only between the parties of the matching capabilities.
Moon is a lamp in the evening. Sun is a lamp in the morning. 'dharma' is a lamp in all the 3 'lokas' (As I know 3 lokas are swarga, pruthvi and paatal). And a good son is a lamp of the whole 'kula' ('kula' is the group of people belonging to the same ancestors).
Here the implied meaning of the lamp is the one which shows a correct path to us. It's correct meaning may be perhaps understood by the samskrit line "tamasoma jyotirgamya" - i.e. Lead us from darkness to the Light.
1) brahmashcharyAshrama :- person is expected to undergo learning (schooling) in this phase .. to earn 'vidyA'.
2) g^RhasthAshrama :- person is expected to live married life/earn money and serve for his family in this phase.
3) vAnaprasthAshrama :- in this phase person is suppose to serve society selflessly and earn 'puNya'.
4) sanyAsAshrama :- leave material life and devote oneself for 'mokSha'.
Meaning of the subhAShita:
One who is not able to earn vidyA (does not pay attention to learning) in first (brahmashcharyAshrama). one who is not able to earn wealth (i.e. not serving his family) in second (g^RhasthAshrama) one who is not able to earn puNya (i.e. is not serving society) in third (vAnaprasthAshrama) what he will do in forth (sanyAsAshrama) .. (i.e. he cant attain 'mokSha').
Even in current context this is applicable because we still can divide life in these four ashrams. only thing which have changed is, now a days while thinking of life, we think about first two ashrams only.
This subhAShita says that we shall do right things in right phases of life. (also says that all these things are of equal importance).