The Environment Agency said it is closely monitoring the situation and has issued flood alerts for the Lower River Lune and Conder between 4pm today, and tomorrow, January 20.
Lancashire County Council said it is preparing to respond to any problems with flooding on the roads, and has been out delivering sandbags in communities that regularly flood.
The Met Office has issued amber and yellow alerts for heavy rain over the next 36 hours.
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Communities across the district that are prone to flooding are also preparing to protect their homes and businesses.
The Environment Agency said: "River levels are rising at the Galgate river gauge as a result of persistent heavy rainfall.
"Consequently, flooding of property/roads and farmland is expected to begin between 16:00 today 19/01/21 and tomorrow, 20/01/21.
"Flooding is expected to affect low lying land and roads from Kirkby Lonsdale to Conder Green including Ingleton, High and Low Bentham, Wray, Hornby, Carnforth, Caton, Halton, Lancaster, Scotforth and Galgate.
"High river levels are possible on the Rivers Greta, Wenning, Hindburn, Roeburn, Keer, Lune, Conder, Burrow Beck and their tributaries.
"Further rainfall is forecast over the next 36 hours.
"We expect river levels to remain high until Thursday evening 20/01/21.
"We are closely monitoring the situation. Our incident response staff are clearing weed screens and checking defences.
"Please avoid using low lying footpaths near rivers and avoid contact with flood water. This message will be updated tomorrow morning, 20/01/21 or as the situation changes."
Lancashire County Council said its highway teams are preparing to respond to any problems with flooding on the roads ahead of weather warnings for heavy rain.
With flood warnings extending into Thursday, people are being warned to expect some disruption to travel, along with the possibility that homes and businesses in some vulnerable areas could experience flooding.
The county council's emergency planners have already been in touch with blue light services, partner councils, utility companies, and voluntary sector organisations in readiness in case major incidents arise.
Highways staff have already been checking locations which are vulnerable to flooding to ensure that highway drains and trash screens are clear, and extra resources are on standby to help if needed.
These include highways staff and contractors who can respond to incidents such as downed trees, or the need to close roads and divert traffic if roads are affected by flooding. Gully wagons are also on standby which are often needed during or after flooding to clear debris which gets washed into highway drains.
People are also being reminded that up to 80% of reports received about problems with drains during severe weather are due to debris sitting over the top of grates, rather than a more serious maintenance issue. If it is safe to do so, clearing the debris which is plugging the grate can often resolve the issue and allow water to enter the drainage system.
The county council maintains over 300,000 roadside drains with those most at risk of becoming blocked being checked most often.
John Davies, head of highways, said: "We always respond to reports of flooding as quickly as we can, and whatever the problem our teams will do their best to help.
"Our teams have already been checking culverts and drains which are vulnerable to becoming blocked, and will be on standby to respond to any reports of flooding we receive.
"During heavy and persistent rain such as has been forecast this week we can expect there to be some surface water flooding, and I would ask people to be very careful on the roads. If you encounter a flooded road, please stop and turn around rather than put yourself at risk.
"As we have seen during past flooding incidents, the sheer volume of water can lead to drainage systems becoming overwhelmed, and it is often the case that the water will only be able to drain away once the storm has subsided and river levels have lowered, so I would also ask people to be patient.
"If people are worried that a highways drain has become blocked by debris it’s worth being aware that this can often be dealt with by brushing the debris aside and clearing it away.
"However, please only do this if it's safe as we would never want anyone to put themselves at risk.
"We do of course respond to all reports of flooding that we receive, but particularly when storms are ongoing we have to prioritise the most serious flooding issues."
If you can't clear a blocked drain yourself, or the problem doesn't appear to be caused by debris plugging the grate, please report it online at lancashire.gov.uk/roads-parking-and-travel/report-it or by calling 0300 123 6701 and highways staff will attend as soon as they can. You can find more information and advice about what to do before, during and after a flood at lancashire.gov.uk/flooding.