It comes as NHS Test and Trace reached its lowest ever proportion of close contacts nationally, with some 40% of people not advised to isolate by contact tracers.
Data from the Department for Health and Social care shows 27,211 people who tested positive for Covid-19 in Lancashire were transferred to the Test and Trace service between May 28 and October 28.
That means 5,748 new cases were transferred in the latest seven-day period.
Contact tracers ask new patients to give details for anyone they were in close contact with in the 48 hours before their symptoms started.
This led to 58,292 close contacts being identified over the period – those not managed by local health protection teams, which are dealt with through a call centre or online.
But just 57.3% were reached – a figure that has fallen steadily over a five-week period.
Across England, 58.5% of contacts not managed by local health protection teams were reached and told to self-isolate by NHS Test and Trace in the latest week to October 28.
Local health protection teams deal with cases linked to settings such as hospitals, schools and prisons.
The contact tracing rate including these cases was 59.9% – a record low.
Around 140,000 new cases were transferred nationally in the week to October 28.
Before the new figures were published, Justice Secretary Robert Buckland said the month-long lockdown that began in England on Thursday will be used to “redouble our efforts” to expand the NHS Test and Trace programme.
Speaking to BBC Breakfast, he said it is also vital to increase the speed at which test results are returned.
“Lots of people are receiving them the next day which is good, but there are still too many people who are having to wait for days and we are going to continue to work to speed that up,” he said.