This is a more or less successful strategy - more, because they do catch up to the Avatar. Less, because she always gets away, and each time they lose her turns into another frustrating hunt for rumors among people who really, really don't like the Fire Nation - and definitely like the Avatar more than them. 

"We might get a bit more if we're not dressed so obviously as Fire Nation..." her aunt muses during one such exceptionally frustrating point, where the local villages (all Earth Nation) are refusing to talk to them. 

Zuko frowns. "That seems like lying." Also she doesn't own any other clothes.

"Is lying always bad?"

"It is usually bad."

"And you'd say it is in this case?"

"The people we're talking to would say so."

"A good way to look at it."

Doesn't answer if it's the right way.

Hard to say if there's any one right way - there's certainly wrong ways, but the world is... Complicated.

And it's something Zuko will have to figure out for herself, too. Iroh can't dictate morals to her.

Complicated. Zuko's... not good at complicated.

She'll need to practice, then. 

Sigh. Nothing's ever easy.

Life would get boring if it was too easy.

If Aunt says so.

It's almost like her niece doesn't believe her...

Huh. Weird.

Very strange!

A mystery for the ages and no mistake. Moving on.

They'll need to find out other ways of getting information on the Avatar, then, if Zuko is unwilling to lie.

...Any suggestions?

When all else fails, there's always bribery.

That doesn't sound very honorable either.

The people they're bribing will approve, though.

Explain?