A LIC is just a company, which happens to have a business centred on investing. The tax reporting and burden is largely the responsibility of the company. As a shareholder, you generally just have to report on dividends (which is very straight forward). A trust on the other hand, is required to distribute all net income, which is made up of a combination on dividends, capita gains etc. This is the reason there are a multitude of entries on a trust AMIT statement.
In relation to your second comment. Yes, the company does pay tax, but they are also able to distribute franked dividends - which avoids double taxation issues.
The biggest myth, particularly with respect to franking credits, is what their net effect is. Fund managers will spruik franking credits as some magical advantage to unfranked dividends, when in reality the net effect is the same.
In simple terms, if I said to you - I will give you $1, but you need to pay me 30 cents - you would instinctively know the net benefit to you is 70 cents. This is the equivalent of a trust distribution. That is, they pay out the income untaxed and then you remit the tax portion.
Alternatively, I could just say here is 70 cents. The 30 cents has already been paid. Again, the net benefit is 70 cents.
At the end of the day, all that matters is your marginal tax rate - which will dictate what portion gets eaten up by tax.
