Your code doesn't match the instruction to the user. The following does what you tell the user:
Console.WriteLine("Choose 7 numbers (1-39) by pressing ENTER after every number:");
int[] userLottery = new int[7];
int i = 0;
while (i < 7)
{
Console.Write("Your choice #{0}: ", i+1);
string userRow = Console.ReadLine();
int userNumber;
if (!Int32.TryParse(userRow, out userNumber) || userNumber < 1 || userNumber > 39)
{
Console.WriteLine("Invalid number! Please try again!");
}
else
{
userLottery[i++] = userNumber;
}
}