A different version with a BUTflag variable to keep track of the button press and release. I have not dealt with the DUMPTIME variable but hopefully this will give you an idea of how to use flags so the logic doesn't fail.

#define DUMP 2          // Pin connected to big dump relay
#define BUTTON 3        // Pin connected to manual dump push button.
#define BUTTONlight 4   // Pin connected to push button light.
#define DELAY 50        // Debounce Time

int BUTstate;           // Current reading from BUTTON pin
int BUTflag = 0; 
int go = 0;
long lastDebounce = 0;  // Last time output was changed

unsigned long DUMPTIME;
unsigned long LOT;
unsigned long prevTIME;

int LOK = 0;

int readTselector(int pin)
// returns the button number pressed, or zero for none pressed 
// int pin is the analog pin number to read 
{
    int c = analogRead(pin); // get the analog value  
    if (c > 1000){
        return 0; // buttons have not been pressed
    }   
    else if (c<1000 && c>600){
        return 1; // button 1 pressed
    }
    else if (c<520 && c>400){
        return 2; // button 2 pressed
    }       
    else if (c>100 && c<400){
        return 3; // button 3 pressed
    }         
    else if (c<100){
        return 4; // button 4 pressed
    } 
    else return 0; // just in case
    }

long DTselect()
{
    switch(readTselector(1)){
        case 0: return 210000; // no buttons pressed
            break;
        case 1: return 180000; // someone pressed a button!
            break;
        case 2: return 150000;
            break;
        case 3: return 120000;
            break;
        case 4: return 90000;
            break;
        default: return 210000; // default
            break;
    }
 }

int LOselect()
{
  switch( readTselector(2) ){
        case 0:  return 20000; // no buttons pressed
            break;
        case 1:  return 15000; // someone pressed a button!
            break;
        case 2:  return 10000;
            break;
        case 3:  return 5000;
            break;
        case 4:  return 0;
            break;
        default: return 20000; // default
            break;
    }
 }

void setup()
{ 
    pinMode(A1, INPUT);
    pinMode(A2, INPUT);

    pinMode (BUTTON, INPUT);
    pinMode (BUTTONlight, OUTPUT);
    pinMode (DUMP, OUTPUT);

    digitalWrite(DUMP, HIGH);
    delay(10000);
    digitalWrite(DUMP, LOW);
    digitalWrite(BUTTONlight, HIGH);
}


void loop()
{
    DUMPTIME = DTselect();
    LOT = LOselect();

    BUTstate = digitalRead(BUTTON);

    unsigned long currTIME = millis();
/*
    if ((currTIME - prevTIME) >= DUMPTIME && !LOK){
        LOK = 1;
        digitalWrite(BUTTONlight, LOW);
        digitalWrite(DUMP, HIGH);
        delay(10000);
        digitalWrite(DUMP, LOW);
        prevTIME = currTIME;
    }
    else */
    if (LOK){
        delay(LOT);
        digitalWrite(BUTTONlight, HIGH);
        LOK = 0;
    }
    else if(!LOK){
        if(!go && BUTstate && !BUTflag){
            lastDebounce = millis();
            BUTflag = 1;
        }
        else if (!go && BUTstate && BUTflag==1 && (millis() - lastDebounce) > DELAY){
            BUTflag = 2;
        }
        else if (!go && !BUTstate && BUTflag==2){
            BUTflag = 0;
            go = 1;
        }
        else if (go){
            digitalWrite(BUTTONlight, LOW);
            digitalWrite(DUMP, HIGH);
            delay(10000);
            digitalWrite(DUMP, LOW);
            prevTIME = currTIME;
            go = 0;
            LOK = 1;
        }
    }
}