The crash happened at about 13:00 GMT on the A607 in Waddington.
Police said the ambulance was responding to an emergency call and had its blue lights on when it was involved in a collision with the two cars. There was no patient onboard at the time.
Four people, including the two ambulance crew, were taken to hospital in Lincoln.
Insp Simon Heads from the Lincolnshire Police serious collision investigation unit said "the two ambulance crew are uninjured".
He added that a female passenger from one of the cars who was taken to the Queen's Medical Centre in Nottingham was "not as seriously injured as was first feared".
East Midlands Ambulance Service NHS Trust has confirmed one of its ambulances was involved in the crash.
The trust said it was "working with Lincolnshire Police to support their investigation".

However, it said the girls abducted from a school in Chibok in April 2014 were not among them.
The military said the girls and women were freed during major operations ending in the seizure of four Boko Haram camps in the Sambisa Forest.
A military spokesman said they were now being interviewed.
Weapons were also seized at the camps taken in the latest operation, the military said.
In recent months Nigerian security forces have taken back most of the territory previously under the control of Boko Haram, the BBC's Tomi Oladipo reports from Lagos.
Gen Chris Olukolade said the hostages were freed as part of a major, ongoing operation.
He said accurate intelligence had helped the military locate the camps, which had been attacked from all directions by ground and air forces.
Last October, the government said it had secured an agreement for a ceasefire and the release of the girls taken from Chibok, but Boko Haram subsequently denied this.
The abduction of the girls in Chibok sparked global outrage with many joining a campaign online to free them using the hashtag #BringBackOurGirls.
Several nations including the US and China vowed to help find them and there have been reported sightings of the girls, but none has been found to date.
Meanwhile, the government of neighbouring Niger gave more details about fighting between its troops and Boko Haram on an island in Lake Chad over the weekend.
It says 28 civilians died when Boko Haram attacked Karamga island and that 46 of its troops died in the battle for the island, along with more than 150 militants. Reports in local media have given a much higher death toll for government forces.
Boko Haram's insurgency, and the army campaign against it, have killed more than 15,500 people since 2012. The violence has recently spread to neighbouring Niger, Chad and Cameroon.
Five people have been taken to hospital following a crash involving an ambulance and two cars in Lincolnshire.
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The Nigerian military says it has rescued 200 girls and 93 women from an area where the Islamist militant group Boko Haram is active.