Lambert conformal conic projection map coordinates

I have a database of locations by lat/long. Trying to overlay on a background image that is a map using the Lambert conformal conic projection. I have the following specs on the map

Map_Projection_Name: Lambert Conformal Conic
Standard_Parallel: 45
Standard_Parallel: 33
Longitude_of_Central_Meridian: -100
Latitude_of_Projection_Origin: 38
False_Easting: 0.000000
False_Northing: 0.000000

Planar_Coordinate_Encoding_Method: Row and column

Abscissa_Resolution: 262.47750
Ordinate_Resolution: 262.46550
Planar_Distance_Units: Meters

Does anyone have the code for correctly mapping the coordinates on the background?

Maybe this helps?
It’s from the Processing’s giCentre Utils library

package org.gicentre.utils.spatial;

import processing.core.PVector;

First two lines in this code above. I found the resource but there is no way to download it. I guess I just don’t know how to navigate around.

No, these imports are standard imports from the library itself. Don’t worry about them.
You have to install the library giCentre first with the tools in the IDE.
You’ll find examples there, but not of the Lambert conformal conic projection.
The lib, however, has such a Class, That’s the link above. You can find and use the methods to use for the projection there. Or even better, see the reference in the library folder at “Processing/libraries/gicentreUtils/reference/index.html”.

The gicentre site has also a Processing library called geoMap, only downloadable there.
Here’s a start.