The incident took place at the B1192 at Langrick, near Boston.
The white Mercedes it allegedly collided with is reported to have been damaged. Nobody was injured.
A police spokesman said: “Following several lines of enquiry, we hope a public appeal may help identify the driver of the van. The incident happened at 8.19pm on 26 September.
“If you have dashcam footage, or witnessed the incident and have information which could help, please contact us on 101, quoting incident 503 of 26th September.”