Hard to give a general answer, as each LIC is a little different. Some always trade at discount (but at varying sizes of discount), some almost always trade at a premium, and many fluctuate between discount and premium over time (this is the case for the biggest ones - AFI, ARG, MLT, BKI etc).
True, its best to buy an LIC at a discount, but remember that the discount is not the be all and end all. Really you need to look at an LIC's history of discount/premium to make a judgement as to how good the current discount is. Bell Potter puts out a report which gives you a graph of discount/premiums for each LIC. Also look at their share price movement and dividend history over time. Also check out what stocks they actually hold, some (like CIN and HHV) hold a high proportion in one particular stock and you need to make sure you're comfortable with that particular stock holding.
If you believe the market is significantly overvalued and likely to drop, then you probably shouldn't invest in an LIC, as its share price will still likely drop with any drop in the market. But a decent discount (for a good LIC that sometimes trades at a premium) may cushion the blow a little. It may also give you an additional boost if the market happens to keep going up and the LIC moves back into premium.