I'm not Spaniard but my understanding of "liarla parda" is a bad connotation, it means having problems, doing a mess so I think it hardly means hanging out and having some fun, may be you or some English speaker can figure out some set phrase for this. Cheers.
Yes, it does have a negative connotation, but as the commenter Pavlorpvo correctly mentioned (I've quoted him just below), this saying acquired a much more comical meaning in Spanish popular culture, when it was mentioned in an Antena 3 television interview, which subsequently became one of Spain's most viral YouTube videos:
Buenas tardes:
Quería incorporar un mensaje creo que de importancia inestimable para el hilo sobre la expresión "liarla parda":
Esta expresión ha tenido un auge reciente e impresionante gracias a un incidente contemporáneo cuya causante fue entrevistada en televisión. En el vídeo, la (presunta) socorrista, que explica un accidente ocasionado por el uso indebido de productos químicos, emplea la expresión "liarla parda" en su más aceptada acepción.
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If you search YouTube with "la he liado parda", you'll get the video straightaway.
The interview came out maybe 6-7 years ago, and in it a young girl who was working as a summertime pool attendant explains how she accidentally mixed chlorine with the wrong pool chemicals and caused a massive cloud of poisonous vapour to come billowing out of the pool. I think the neighbourhood had to be evacuated. The poor girl gave an interview and during it she said, "Que vamos que la he liado parda" in a frustrated attempt to try and explain which chemicals she has mixed together. The effect is highly comical because she tries to explain what she did, but doesn't really have the vocabulary or chemistry know-how or terminology to express it precicely. So she ends up telling the story in colloquial Spanish (ending with "la he liado parda") and all the while you see the flashing emergy vehicles in the background and images of toxic clouds... you have to watch it to appreciate it.
Before this video went viral, the saying was previously unknown in many parts of Spain, being more typical to this girl's region (around Valencia if I'm not mistaken).
But now, as the user Pavlorpvo correctly says, thanks to the video, the phrase "la he liado parda" has acquired a whole new dimension and has become firmly embedded in Spanish popular culture/language. It's now often used among friends in comical/fun/funny situations, from going out partying and getting drunk to making a mistake of any sort.
As to the gender, "la" refers to "situación" or "cosa", which is feminine, as Rastrom also mentions:
Todo depende del contexto de la expresión.
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Respecto al género de la expresión, es femenino porque se refiere a una situación o a una cosa, ambas femeninas.