Question: Suppose the winning combination consists of $7$ digits, each digit randomly ranging from $0$ to $9$. So the probability of $1111111$, $3141592$ and $8174249$ are the same. But $1111111$ seems (to me) far less likely to be the lucky number than $8174249$. Is my intuition simply wrong or is it correct in some sense?

Answer: 
Another argument in favor of choosing a random-looking number is the following: suppose 1111111 is drawn. The scientifically uneducated audience will likely complain that it "can't be random" and something went wrong (or maybe that you cheated), and in the end they'll have the draw cancelled or repeated.

Sadly, there's no arguing against that --- I bet you can convince the average judge and jury that "1111111 is not random".

(That said, in real life 1111111 *is* indeed more likely to appear than 8174249, since a mechanical or programming error in the drawing machine could make it more likely to have repeated numbers drawn than completely random ones).

In short, real life is not like mathematics. :)
In canada, lottery tickets are manually drawn and each number cannot be drawn more than once.

For instance, Loto 6/49 (6 numbers, 1 to 49), an "human instution" inprobable number would be 1-2-3-4-5-6 (6 number in a row) and I beleive this is less probable then a more general number like 1-11-20-30-31-45.

Why? Because of the way it's drawn. If the number were drawn all at once by a computer for instance, I wouldnt beleive this. However, it's not the case in this example. Each time a number is drawn, it gets removed from the pot and the pot is scrambled again. Thus, there less numbers in the first 10 digits after each draw, making them less likely to be drawned. 

Call me crazy, but I would never bet my money on a ticket that has 6 numbers in a row.