How to implement synchronization in multi threading with python and ROS Services?

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Im trying to implement multi threading (parallel processing) with python and using mutex threading. I have first process that check the Pressure Value and the modem update(in the code implemented with odom_callback and callback_modem functions), and second process that calls ROS SERVICES ( in the code implemented with ros_serice_server server and imu_client client functions). Here is the implementation code in python

#!/usr/bin/env python3

from __future__ import print_function
import rospy
import numpy as np
from os import system
import time
import threading
import Microcontroller_Manager_Serial as Serial
import IMU_Functions as IMU
import Motors_Functions as Motor
import Pressure_Functions as Pressure
from geometry_msgs.msg import Vector3
import Modem_Functions as Modem
import threading 
import time
import serial
import serial.tools.list_ports
from time import sleep
from std_msgs.msg import Float32
from std_msgs.msg import String
from demo_teleop.srv import ImuValue,ImuValueResponse

P0 = 1.01325 #Default Pressure 
mutex = threading.Lock()
Communication_Mode_ = 0
pub_pressure = rospy.Publisher('depth',Vector3,queue_size=1)
pub_modem = rospy.Publisher('modem_data',Float32,queue_size=1)

def handle_ros_services(req):
    mutex.acquire(blocking=True)
    print("Server Read Data:")
    global T0
    data_received = Pressure.Pressure_Get_Final_Values(1,1)
    #print("Server Read Data:")
    T0 = (np.int16((data_received[6]<<24) | (data_received[7]<<16) | (data_received[8]<<8) | (data_received[9])))/10000
    T=T0
    temperature = T
    current_x_orientation_s = temperature
    print("Returning Service Temperature Data", current_x_orientation_s)
    return ImuValueResponse(current_x_orientation_s, True)
    mutex.release()

def ros_serice_server():
    s = rospy.Service('imu_value', ImuValue, handle_ros_services)
    print("Ready to get_value")

def odom_callback():
    # reentrang processing
    mutex.acquire(blocking=True)
    # work serial port here, e.g. send msg to serial port
    global P0
    data_received = Pressure.Pressure_Get_Final_Values(1,1)
    #P1 = (np.int16((data_received_pressure[6]<<24) | (data_received_pressure[7]<<16) | (data_received_pressure[8]<<8) | (data_received_pressure[9])))/10000
    P1 = (np.int16((data_received[6]<<24) | (data_received[7]<<16) | (data_received[8]<<8) | (data_received[9])))/10000
    #P0 = (np.int16((data_received_pressure[6]<<24) | (data_received_pressure[7]<<16) | (data_received_pressure[8]<<8) | (data_received_pressure[9])))/10000
    P0 = (np.int16((data_received[6]<<24) | (data_received[7]<<16) | (data_received[8]<<8) | (data_received[9])))/10000
    P = P0 # Relative Measured Pressure
    feedback =Vector3()
    feedback.x = 0    #Angular Velocity
    feedback.y = 0
    feedback.z = P/9.81 #Depth
    pressure = feedback.z
    print("Pressure : ", pressure)
    pub_pressure.publish(feedback)
    # reentrant processing
    mutex.release()

def callback_modem(event):
    # reentrant processing
    mutex.acquire(blocking=True)
    # work serial port here, e.g. check for incoming data
    event = Serial.Serial_Port_Receive_Data(20,0.2)
    if (event == 1): # Received data from acoustic modem
        modem_data= event
        pub_modem.publish(modem_data)
        print("received ")
    else:
        print("not received...... ")
    mutex.release()

if __name__ == '__main__':
    # initialize serial port here
    Serial.Serial_Port_Standard()
    rospy.init_node('imu_value')
    ros_serice_server()
    rospy.Timer(rospy.Duration(1), callback_modem) 
    while not rospy.is_shutdown():
        try:
            odom_callback()
        except:
            print('pass')

And the client node

#!/usr/bin/env python3

from __future__ import print_function
import rospy
import sys
import numpy as np
from os import system
import threading
import Microcontroller_Manager_Serial as Serial
import IMU_Functions as IMU
import Motors_Functions as Motor
import Pressure_Functions as Pressure
from geometry_msgs.msg import Vector3
import Modem_Functions as Modem
import time
import serial
import serial.tools.list_ports

from time import sleep
from std_msgs.msg import Float32
from std_msgs.msg import String
from demo_teleop.srv import ...