It should pay 100USD for every 713 shares (diff as I type).
That refers to shares of a certain difficulty: diff 1 Litecoin shares or diff 65,536 shares according to some mining clients (notably CGMiner).
Each found share has its difficulty. If the share's difficulty is equal to or higher than the worker's difficulty, it gets submitted by the worker and accepted by the pool.
At 713 difficulty, it will take on average 713 * 65,536 = 46,727,168 diff 1 shares to find a block. Likewise, it would take 713 * 65,536 / D diff D shares.
Note that, if you submit a diff 256 share at 128 worker difficulty, you get paid for a diff 128 share. So, assuming your worker difficulty is constant (LTC pools tend to use variable difficulty), your expected payout would be numbers of shares * worker difficulty * 50 / difficulty LTC, where both worker difficulty and difficulty should use the same metric (just use the values the mining client reports).
Aren't the mechanisms supposed to be very similar?
For Bitcoin mining, a diff 1 share (lowest possible worker difficulty) is found for every 232 hashes that are calculated. Since Litecoin's scrypt algorithm is about 1000 times slower than SHA256, mining Litecoins would have a very high variance if the same metric of worker difficulty was being used.
Therefore, pools and mining clients implemented shares with worker difficulty lower than 1, e.g., diff 2-10.
In order to avoid dealing with fractional difficulties (I assume), mining clients labelled diff 2-16 shares diff 1 shares, so actual diff 1 Litecoin shares become diff 65,536 shares.
Litecoin difficulty is very low!
Since computing hashes is 1,000 times slower for Litecoin mining, a difficulty of 713 for Litecoin mining is more or less equivalent to a difficulty of 713,000 for Bitcoin mining.