In theory, the underlying mechanisms of the Web make no difference between a browser getting data and displaying it to you, and your LWP-based program getting data and doing something else with it. However, in practice, almost all the data on the Web was put there with the assumption (sometimes implicit, sometimes explicit) that it would be looked at directly in a browser. When you write an LWP program that downloads that data, you are working against that assumption. The trick is to do this in as considerate a way as possible.
When you access a web server, you are using scarce resources. You are using your bandwidth and the web server's bandwidth. Moreover, processing your request places a load on the remote server, particularly if the page you're requesting has to be dynamically generated, and especially if that dynamic generation involves database access. If you're writing a program that requests several pages from a given server but you don't need the pages immediately, you should write delays into your program (such as sleep 60; to sleep for one minute), so that the load that you're placing on the network and on the web server is spread unobtrusively over a longer period of time.
If possible, you might even want to consider having your program run in the middle of the night (modulo the relevant time zones), when network usage is low and the web server is not likely to be busy handling a lot of requests. Do this only if you know there is no risk of your program behaving unpredictably. In Chapter 12, "Spiders", we discuss programs with definite risk of that happening; do not let such programs run unattended until you have added appropriate safeguards and carefully checked that they behave as you expect them to.
While the complexities of national and international copyright law can't be covered in a page or two (or even a library or two), the short story is that just because you can get some data off the Web doesn't mean you can do whatever you want with it. The things you do with data on the Web form a continuum, as far as their relation to copyright law. At the one end is direct use, where you sit at your browser, downloading and reading pages as the site owners clearly intended. At the other end is illegal use, where you run a program that hammers a remote server as it copies and saves copyrighted data that was not meant for free public consumption, then saves it all to your public web server, which you then encourage people to visit so that you can make money off of the ad banners you've put there. Between these extremes, there are many gray areas involving considerations of "fair use," a tricky concept. The safest guide in trying to stay on the right side of copyright law is to ask, by using the data this way, could I possibly be depriving the original web site of some money that it would/could otherwise get?
For example, suppose that you set up a program that copies data every hour from the Yahoo! Weather site, for the 50 most populous towns in your state. You then copy the data directly to your public web site and encourage everyone to visit it. Even though "no one owns the weather," even if any particular bit of weather data is in the public domain (which it may be, depending on its source), Yahoo! Weather put time and effort into making a collection of that data, presented in a certain way. And as such, the collection of data is copyrighted.
Moreover, by posting the data publicly, you are almost definitely taking viewers away from Yahoo! Weather, which means less ad revenue for them. Even if Yahoo! Weather didn't have any ads and so wasn't obviously making any money off of viewers, your having the data online elsewhere means that if Yahoo! Weather wanted to start having ads tomorrow, they'd be unable to make as much money at it, because there would be people in the habit of looking at your web site's weather data instead of at theirs.
Before you start pulling data off of a web site, you should put good effort into looking around for its terms of service document, and take the time to read it and reasonably interpret what it says. When in doubt, ask the web site's administrators whether what you have in mind would bother them.