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. Some LICs permanently 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). Bell Potter puts out a report which gives you a graph of historical discount/premiums for each LIC over time. Most of the biggest ones seem to be trading pretty close to their NAVs at the moment, so they're not overpriced but not a bargain either.
You should also look at their share price movement and dividend history over time. Also check out what stocks the LICs actually hold (each LIC publishes their top 20 stocks monthly in their company announcements available on the ASX), some (like CIN) hold a high proportion in one particular stock and you need to make sure you're comfortable with that particular stock holding. Some hold higher proportions of stocks in particular industries too (eg ARG holds less of the big 4 banks than the other big ones like AFI).