It is entirely possible to have a non-whiny, non-sanctimonious Lawful Good character; unfortunately this tends to be rarer than it ought to be.

Paladins, for instance, lose their powers if they associate with evil-aligned people; this means that they are likely to be constantly on the lookout for signs of evil behavior in their companions.

Lawful characters are, in general, more likely to interfere in the actions of others because of their stronger belief in the universal applicability their own beliefs. This sometimes combines with the good alignment to create sanctimonious characters.

One problem is that some Lawful Good characters display an alignment derided as Lawful Stupid, behaving in ways that are flatly foolish and that have little or nothing to do with morality.