The court heard that her condition quickly deteriorated and she was pronounced dead 17 hours after being admitted to Rotherham Hospital.
South Yorkshire coroner Nicola Mundy said Mrs Lockwood had been "extremely unlucky".
At Doncaster Coroner's court, she recorded the cause of death as Vaccine-Induced Thrombotic Thrombocytopenia (VITT) and returned a verdict of misadventure.
Little was known about the link between the Covid-19 jab and VITT at the time of Mrs Lockwood's death, the coroner said, but "medical advances" meant the condition was better-recognised since the initial vaccine rollout.
Government figures show the type of reaction Mrs Lockwood experienced is considered extremely rare. There have been 438 reported cases and 78 deaths after an estimated 24.9 million first doses and 24.2 million second doses of the AstraZeneca vaccine.
The inquest heard administrative secretary Mrs Lockwood first went to Rotherham Hospital's A&E on 22 March but left without being seen after a long wait.
She returned the next morning suffering from debilitating headaches, blurred vision and vomiting, and by midday could not speak in full sentences.
By 2am on March 24, the mother-of-two was unresponsive and her family was called to say their goodbyes.
Ms Mundy said an MRI scan should have been arranged sooner, but this, combined with other measures such as a blood platelet transfusion and lumbar puncture would not have saved Mrs Lockwood due to the massive, "sudden and catastrophic" bleed on her brain.
The inquest also heard Mrs Lockwood had been diagnosed with Idiopathic Intracranial Hypertension (IIH) in 2016, and she had initially assumed this to be the cause of her headaches.
But Ms Mundy said the condition, characterised by intense pressure in the head caused by a build-up of fluid behind the eye, had not been the cause of her death.
A family tribute read during the hearing said Mrs Lockwood - who had two sons - Jayden, 14, and Jax, seven - was "kind, fun-loving and always the first and last on the dance floor at parties".
Rotherham Hospital NHS Foundation Trust said more was now known about the link between the vaccine and VITT and how to treat it, with all patients with low platelets referred to haematologists.
Susan Douglas, of the trust, said lessons had been learned and measures such as extra ward audits had been introduced since Mrs Lockwood's death.
The Government has repeatedly stated that the benefits of vaccines outweigh the risks in the majority of people.