Effect of internet connection speed on solo mining
With solo mining, all you need to get from the Internet is the latest block. Since these come once every 2.5 minutes (average) and are at most 250 KB (typically ~10 KB), you should be just fine. You'd also want to get all the latest Litecoin network traffic in order to validate all the transactions you can, but that'd be pretty small, like the blocks.

You might find (on average) a few more stale blocks than the typical high-speed user, but this shouldn't be too significant: on the order of (your latency and download time - normal latency and download time)/2.5 minutes