I have been trying the trial of the app, and it works, however it seems to only work in the last pass app. There is no integration with the default browser in honeycomb. When you open a site from last pass, so that it loads your saved credentials, it seems to load in a special last pass browser, not the default android browser.
This browser does not seem to support tabs, or even save your current page when you try to switch apps or go to the home screen. What last pass needs is integration with the chrome like browser in honeycomb, which does support addons.
Lastpass doesn't have tabs and really isn't optimized for the Xoom yet. As IamJAd said, Dolphin is decent, it has a great lastpass addon. Although DHD has some scrolling issues, and I feel like their browser is a little clunky compared to the stock browser.
I'm sure when Google gets extensions in the Android Browser its going to be a game changer.