One of the meetings will focus on the junction of Boston Road (A1253) with the A158.
It follows stinging criticism from businessman Patrick Cordingley that problems with traffic lights are driving potential investment away from the town.
Councillor Davies is also due to hold a second meeting about other matters.
Horncastle’s County Councillor Bill Aron is drawing up a list of questions to ask Coun Davies.
Coun Aron is urging town councillors and residents to come forward with more questions.
The meetings come after the News revealed last week that County Council contractors will only carry out repairs at the A158/Langton Hill/West Street junction with a ‘police presence’ in place.
The County Council claims workers were recently put at risk by drivers ignoring red lights.