An amber weather warning is in place for the county from 05:00 GMT to 21:00.
The Lincolnshire Resilience Forum (LRF) said the storm could bring gusts of up to 80mph in some areas, leading to possible damage to property, train cancellations and power cuts.
People have also been warned not to venture too close to the sea.
It comes after Storm Dudley caused widespread travel disruption and power cuts on Wednesday.
The LRF, which includes emergency services and council officials, said there was potential for Storm Eunice to cause further problems.
Mark Garthwaite, emergency planning officer, said: “The main advice we are giving at the moment is for people not to travel unless its absolutely necessary.
“People are safest within their homes.”
Mr Garthwaite said the storm was expected to hit the south of the county first, with other parts seeing stronger winds at various times until the early afternoon.
He said gusts of up to 80mph were possible in “isolated places”, including along the coast.
He said anyone needing to travel should let someone know the details of their journey.
“The emergency services and other authorities are going to be really busy during the day, so we just ask that people be patient – stay safe and only use emergency numbers if they really have to,” he added.
Scott Snowden, resort manager for Cleethorpes, said there was a temptation for people to visit the coast during a storm to see the “full force of mother nature”.
However, he said: “Be aware, waves can take you away in a second.”
He said there was also a risk from debris “thrown up by the sea”.
The Environment Agency has also urged people not to put themselves in danger by taking “storm selfies”.
Ian Brooks, from Western Power Distribution, which covers parts of the area, said extra staff were being brought in to deal with any disruption.
He said the firm was “well-prepared” but advised people to charge up electronic devices in advance as a precaution.
Meanwhile, train operators EMR and LNER said the storm was expected to cause disruption to services, including short-notice cancellations and extended journey times.
Brylaine Travel, based in Wyberton, near Boston, has suspended all bus services on Friday, while Boston Central Park will close at midday.
Burghley House, near Stamford, also said it would be closed due to the “severe weather forecast”.
Storm Eunice will be the fifth named storm of the 2021-22 UK season.
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