This script builds a rotation matrix based on 3 selected verts. It then calculates the euler angles.

rotationAnglesFromMatrix.py

#python
import lx
import lxu.vector
import math

# this something I got from stackoverflow some time ago
# if you'd like to know more about it have a look at this: http://www.soi.city.ac.uk/~sbbh653/publications/euler.pdf
def getRot2(m):
    if m[0][0] == 1.0:
        x = math.atan2(m[0][2],m[2][3])
        y = 0
        z = 0
    elif m[0][0] == -1.0:
        x = math.atan2(m[0][2],m[2][3])
        y = 0
        z = 0
    else:
        x = math.atan2(-m[2][0],m[0][0])
        y = math.asin(m[1][0])
        z = math.atan2(-m[1][2],m[1][1])
    return ( math.degrees(z), math.degrees(x), math.degrees(y))

def getRotAngles():
    # 'select' layer for layerservice
    mLayer = lx.eval('query layerservice layers ? main')

    # get selected verts
    lx.eval('select.type vertex')
    selVerts = lx.evalN('query layerservice verts ? selected')
    
    # check if there are 3 verts selected
    if len(selVerts) != 3:
        # replace with a dialog to make it more user friendly, I'm to lazy right now ;)
        lx.out('Please select exactly 3 vertices!')
        return
    
    # get vert positions
    v0Pos = lx.eval('query layerservice vert.wPos ? %s'%selVerts[0])
    v1Pos = lx.eval('query layerservice vert.wPos ? %s'%selVerts[1])
    v2Pos = lx.eval('query layerservice vert.wPos ? %s'%selVerts[2])
    
    # !!! you should check at this point that the vectors are not collinear !!!
    # this means that they are not in a straight line, again I'm to lazy ;)
    
    # create rotation matrix
    # calculate vec0
    vec0 = lxu.vector.normalize(lxu.vector.sub(v1Pos,v0Pos))
    # calculate a temporary tvec1
    tVec1 = lxu.vector.sub(v2Pos,v0Pos)
    # cross product of vec0 and tvec1 will calc vec2 which is perpendicular to vec0 and tvec1 as well as vec1
    vec2 = lxu.vector.normalize(lxu.vector.cross(vec0,tVec1))
    # cross product of vec0 and vec2 will calc vec1
    vec1 = lxu.vector.normalize(lxu.vector.cross(vec0,vec2))
    # add them to a rotation matrix
    rotMat = (vec0,vec1,vec2)
    lx.out(getRot2(rotMat))
    
getRotAngles()