Hola Kevin

It's a similar sentence and both of them are grammatically correct, but bear in mind that their meanings are different: 

1. Mi amiga estaba perdida en un desierto.

This means "she was lost" in the desert. It reflects the result of an action (how she ended up after getting lost: she was lost.

2. Mi amiga se perdió / se perdía en el desierto.

This means that "she got lost" in the desert. It reflects the action of getting lost.

I hope you can see the difference (the same difference as in the English sentences)

Saludos