Aya Hachem, 19, was shot in broad daylight as she was out shopping close to the Lidl supermarket on King Street in Blackburn on Sunday (May 17).
Emergency services attended and she was taken to hospital but was pronounced dead a short time later.
A subsequent post-mortem examination has revealed that Aya died as a result of a gunshot wound to her chest.
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Two men aged 31 and 35 have been arrested on suspicion of murder and a man aged 29 has been arrested on suspicion of assisting an offender.
They were all detained in the Blackburn area yesterday evening (May 19) and all are in custody.
Senior Investigating Officer, Det Supt Andy Cribbin from Lancashire Constabulary’s Force Major Investigation Team (FMIT) said: “While we have now arrested a number of people as part of this investigation our enquiries are very much on-going and we continue to have a large team of officers and staff working around the clock to find out who was responsible for Aya’s death.
"Our determination to get justice for her family remains undimmed. Our thoughts are very much with Aya’s loved ones and her family are being supported by specially trained officers.
"I would like to thank those who have come forward to assist the investigation so far and I would continue to ask that anyone who has any information, however insignificant they may think it is, to get in touch.
"This is an absolutely tragic loss of a young life and we need to find out what happened – you may hold the key to help us do that so please don’t hesitate to contact us."
It is known that before she was fatally shot, a light silver/ green Toyota Avensis drove past Aya.
Shots were fired from the vehicle, with one of the shots striking Aya in the chest, fatally injuring her.
Officers believe she was not the intended target of the attack.
The Avensis, registration number SV53 UBP, was recovered by police on Sunday (May 17) on Wellington Road.
Three men aged 39, 33 and 36, from Blackburn were arrested on suspicion of murder on Monday (May 18).
They remain in custody.
Detectives are aware of a number of videos circulating across social media and are asking people to report them to the police.
Det Supt Cribbin added: "We know a number of videos of the incident are on social media and it is important that if people are aware of any footage that they formally report this to us if they haven’t already done so as they are potential evidence.
"We would also ask people, even if they are well intentioned, not to share these videos out of respect for Aya and her family.
"Similarly, I would urge people not to speculate online about the cause of or motivation for the incident and to instead share what they know with us, as their information could prove vital."
A police presence remains in the area around the shooting whilst enquiries continue.
The incident is not being treated as terrorism-related or a racially-motivated.
Any information or video footage can be sent to police via the major incident portal at https://mipp.police.uk/operation/0401020120E05-PO1
Anyone with any other information is asked to get in touch with police by calling 101, quoting log number 0412 of May 18.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555 111 or online at crimestoppers-uk.org.