Hi,
I tried implementation as you suggested. And, I was able to implement it using 'Content Query Webpart'. 'Content Query Webpart' allows you to get the data from other sites and also, allows the filter based on sitecolumns.
As Content Query Webpart only allows filter on site columns, I created a sitecolumn of Person, based on the Person lookup list. Then I created a product contenttype with person sitecolumn. Then, added the contenttype to product list. Added the data to it.
Then added the Content Query Webpart to subsite. Added the filter on person sitecolumn with the person name.
Webpart displays the products with the filter on person name.
I hope it helps.
Cheers ...
Rajendra