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Ravi Nair, you would get many answers on your questions, ranging from BS (priti) to honest (haviZsultan).
Lyari is right next to Karachi's business district and is settled mainly by Baluch people. They have been PPP voters for a long time. Seen as counter-weight to MQM gangsters, they enjoyed patronage from PPP, until the Lyari gangsters became too big and went out of control.
MQM, PPP, and ANP each have a role to play in this mess. Each of them have an armed wing, and each has patronized criminals (extortionists, dacoits, and land-grabbers), and each has ethnic support. MQM has support from Urdu-speaking sections of Karachi. PPP enjoys support of Sindhis and Balochis. ANP rode a wave of Pashtun migration to Karachi and thus is a relatively new player.
PML-N does not have much support in Karachi, and that is why it has been able to lead an operation without raising too many heckles. PTI would likely be a beneficiary if an operation is successful in curbing violence, since it has no armed wing and has been targeted by suspected MQM target killers.
What happens after the operation remains to be seen, since it has yet to enter its third and last phase. But I think that there would be a need for subsequent operation. One operation would likely not get desired results.
Karachi used to be the most peaceful city. Now it is the most violent, thanks to crooked ethnic politics. I have not yet discussed religious parties and their contribution, but the ethnic angle is the strongest and most significant.