while both things your looking at have low-res screens, the lenovo screen or any other 15.6" screen with that resolution won't look very sharp (same # of pixels over a larger area = fewer pixels/inch). She may or may not care about that.
Also, know that all the HD content you watch on any screen with that resolution will get downscaled, and won't be HD anymore. Unavoidable though unless you step up to a better resolution.
I haven't used a chromebook, but I believe if you were to go to the app store on chrome on your computer you'd get a feel for everything that's available to you. In that sense, yes, it's like a phone where you're limited to apps. You cannot run windows or mac software on it. Anything that works in browser (facebook games for instance) are fine.
as for the celeron, i've seen a few reviews that say it's fine for streaming.
For alternatives, I just noticed the lenovo S series at 13.3" is under $400 right now on sale (with tax more like $375). Dell has nothing small for less than $400, and neither does HP, to give you a feel.
There are also a lot of notebooks on newegg, you can sort by price, screensize, processor, OS etc.
lastly, I'd recommend going to a store and just playing with what they have there to get a feel for size and features. I like to hold things before I buy them, but that's just me.
edit: if you want to compare processors, i'd use this list (
http://www.notebookcheck.net/Sorting-by-processor.2675.0.html) just use ctrl-f in your browser to find the ones you want to compare, select them, then choose 'restrict' at the bottom, and it'll show you benchmarks.