Draw polygon on LCD from GPS latitude and longitude
Over a small area lat and long are just simple Y and X coordinates respectively.

Dynamic scaling of the points is a very simple matter.  All you need to do is work out the range of each dimension - so subtract the lowest latitude from the highest, and the lowest longitude from the highest.

That gives the full X and Y dimension of your area. Then just divide those by the dimensions of your screen.  That gives you a scaling factor for each direction.

For each point, subtract the lowest longitude and latitude, and divide by the scaling factor for each direction.

If you want to be more fancy and retain the aspect ratio then you just need to work out which of the two scaling factors will allow all the polygon to remain on the screen - that is, divide and offset all your points by one factor, then by the other, and pick the smallest factor where all the points are within the area of your screen.