The alleged assault took place at around 8pm on Tuesday (June 14) close to Ingram Memorial in Market Place, Boston where two men are alleged to have approached the victims, aged in their 20s, and punched and kicked them to the head.
One of the victims has suffered bruising to his brain and the other has a broken jaw.
The suspects were both were wearing dark coloured tracksuits.
It is believed that there was a crowd of around 10 to 15 people nearby during the assault who will have witnessed this incident, or perhaps captured some of it on mobile phones.
Some of those in the crowd are believed to have attempted to intervene and officers are now keen to speak with them to take their statements.
A police spokesman said: “We would also like to hear from anyone who may have captured dashcam footage.
"If you witnessed the incident or captured dashcam footage of the incident, or if you have any information about the incident offenders, please contact us to help with our enquiries.”
If you have any information relating to the incident, call Lincolnshire Police on 101, quoting incident 458 of 14 June, or email [email protected]
If you wish to remain anonymous, you can report via the independent charity CrimeStoppers on 0800 555 111 or online here.