The arguments for transform is lon first then lat. Also, transform method is depreciated, instead you can use the following
import pyproj
proj_daymet = "+proj=lcc +lat_0=42.5 +lon_0=-100 +lat_1=25 +lat_2=60 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs" #my custom CRS
lat = 31.177685
lon = -87.103554
pyproj.Proj(proj_daymet)(lon, lat)
# output: (1192750.1882841575, -1114999.8438182664)