I think the problem might be related to the font being rendered using different rasterizers. In your web browser you're seeing the font rendered using your machine's ntaive rasterizer (OSX or Win), but Photoshop is using it's own internal rasterizer.
Lucida Grande is a well hinted TrueType font, and it looks to me like you're seeing the hints being interpreted differently (or on a Mac, seeing the results of downsampling.) In particular, note in your example how the ascenders are 1 pixel taller than the caps in the HTML version, but the ascenders align with Caps in your version. This could be a result of hints being applied differently.
In that case, you won't be able to get the exact same image in your browser as in Photoshop even if the fonts are exactly the same, but they should be close.
Jason
I would agree with Jason that the difference you see is due to the rasterizer. Lucida Grande will look different still when viewed in a Windows or Linux browser, due to the different rendering engines on those systems.
You can only count on "Lucida Grande" being installed on Mac OS X systems, since it's the main UI font and I don't think you could delete it even if you wanted to. But Lucida Grande is just a newer version of Lucida Sans with an incredibly large character set. There is a similar version of Lucida Sans included with Windows 2000/XP called "Lucida Sans Unicode." Finally, the basic Lucida Sans ships with Microsoft Office products and thus can commonly be found on many Windows and Mac systems. It also has a true italic, which Lucida Grande and Lucida Sans Unicode lack.
The most interesting thing about the three different versions is that while their common glyphs share mostly identical outlines, each one is hinted differently, giving it a noticeably different look when rendered at smaller sizes (at least under Windows).
So, for cross-platform rendering on a website, you might write your style definition like this:
font-family: 'Lucida Grande', 'Lucida Sans', 'Lucida Sans Unicode', sans-serif;
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