Three-number lottery simulator
Using method return types

Instead of relying on static int[] arrays, you should return the appropriate results from getting the user input and generating the lottery numbers so that their interaction is slightly clearer.

Validating user input

Scanner.nextInt() throws an InputMismatchException when the next input is not parsable as an integer. You should have a method that handles that safely.
For example (prompted by @KonradMorawski's comment):

private static int getInteger(Scanner scanner) {
    System.out.println("Enter an integer:"); 
    while (!scanner.hasNextInt()) {
        System.out.println("Not an integer, please try again.");
        scanner.next();
    }
    return scanner.nextInt();
}


Comparing arrays

Arrays.equals(int[], int[]) can be used to compare two int[] arrays.

Using other types for comparison

You may also want to consider using other types to compare the lottery numbers. For example, a plain integer works as well:

private static int getNumber(int a, int b, int c) {
    return a * 100 + b * 10 + c;
}


edit:

try-with-resources

If you are on Java 7 and above, you should use try-with-resources for efficient handling of the underlying I/O resource:

public static void main(String[] args) {
    try (Scanner scanner = new Scanner(System.in)) {
        // ...
    }
}