Were you using webmail (yahoo, gmail, Hotmail, etc) in Outlook? If so, then your contacts are included with your account and will follow you with any email software client you choose to use.
If you were not using webmail, then according to
https://support.mozilla.org/en-US/kb/switching-thunderbird#w_switching-from-outlook-2007-to-thunderbird, it appears it would be best for you to log into XP, install Mozilla Thunderbird, and import your contacts into Thunderbird. From there, I imagine your contacts would be in a Thunderbird format that you could export and bring into your Linux Lite version of Thunderbird.
If you can no longer log into XP, then you might be able to get a version of Outlook installed in Linux Lite using the Wine program (found in Lite Software). If Outlook opens successfully, you could point Outlook to the address book file/folder on the XP part of your hard drive. It's messier, but still an arrow in your quiver. But personally, I hope either of the first two paragraphs represent your situation.