I have read pretty confusing (at least to me) descriptions on how to connect a DYP-ME007 Ultrasound Range finder, and it's really dead simple. Ditto the I2C LCD. I use a DFRobot LCD. No resistors, pull-up, -down or any other direction are needed   . You do need the LiquidCrystal_I2C on your path (get it fromhttp://hmario.home.xs4all.nl/arduino/LiquidCrystal_I2C/LiquidCrystal_I2C.zip here and unzip it to the libraries subfolder of your arduino development environment folder (the subfolder of the one that contains the arduino.exe). The DYP-ME007 has 5 pins, and you'll need only four: Vin, GND, TRIG and ECHO. Vin and GND are obvious and for teh script here, TRIG goes on digital 2 and ECHO to digital 3, but you choose. The LCD I2C is really simple too. Just connect Vin and GND, the SCL clock line goes on analog 5 and the SDA data line on analog 4. Hook it all up, connect your board to USB, upload this script and enjoy  
 

/* This Arduino script uses the DYP-ME007 Ultrasound Range finder to
 * measure distance in cm and displays the distance on a DFRobot
 * I2C LCD Module 508040.
 * Hardware: Connect the DYP-ME007 to +5V and Ground, and
 * the dypOutputPin to the DYP_ME007 "Trig" pin and the 
 * the dypInputPin to the DYP-ME007 "Echo" pin. 
 * By default I2C chips use analog pin A4 for data SDA and A5 
 * for the clock SCL. Of course 5V and GND need to be connected too.
 * Credits to DFRobot and Bexilino on http://arduino.cc/forum/index.php?topic=60973.0
 * from which I have copied parts.
 */
 
#include <Wire.h> 
#include <LiquidCrystal_I2C.h>

LiquidCrystal_I2C lcd(0x27,16,2);  // set the LCD address to 0x27 for a 16 chars and 2 line display

int dypOutputPin = 2; // TRIG 
int dypInputPin = 3;  // ECHO 
long distance;
long cm;

void setup(){
  pinMode(dypOutputPin, OUTPUT);
  pinMode(dypInputPin,INPUT);
  lcd.init();                      // initialize the lcd 
  lcd.backlight();
}

void loop()
{
  // The DYP-ME007 pings on the low-high flank...
  digitalWrite(dypOutputPin, LOW);
  delayMicroseconds(2);
  digitalWrite(dypOutputPin, HIGH);
  delayMicroseconds(10);
  digitalWrite(dypOutputPin, LOW);   
  // the distance is proportional to the time interval
  // between HIGH and LOW
  distance = pulseIn(dypInputPin, HIGH); 
  cm= distance/58;                        
  lcd.clear();
  lcd.print(cm);
  delay(100); // avoids LCD flicker

}