A car, driven by a man known to Lisa, was later found abandoned on the Queen Elizabeth II Bridge at Dartford.
Police say a handgun was found inside the vehicle, and enquiries have since established that the suspect entered the water below.
Image: Flowers were left at The Three Horseshoes pub over the weekend
In an update on Thursday, Detective Chief Inspector Dave Higham, from Kent Police, said: “We have carried out a full and extensive investigation into Lisa’s tragic murder and our enquiries have concluded that the suspect is believed to have died after falling into the River Thames.
“Multiple searches of several areas of the river have since been assisted by the Metropolitan Police, London Fire Brigade and Coastguard, but at this stage we have not recovered a body.
“These searches are ongoing and whilst our investigation will continue, we will be preparing our findings and reports to assist the coroner.
“This murder has led to the senseless loss of a beloved daughter and mother and our thoughts remain with Lisa’s family.”
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CCTV captures sound of gunshots near fatal shooting site
While officers said the victim and suspect were known to each other, they have not revealed how they are connected.
Michelle Thomas, who runs The Three Horseshoes pub near Sevenoaks, told Sky News she heard two loud bangs that she initially “thought were fireworks” on the night of the shooting.
She said there was “so much commotion – screaming, shouting, crying” and the attack had left the community in “absolute shock”.
She said the victim, Ms Smith, had been to the pub before “mostly in the summer” but “wasn’t a regular”.