Upvote:4
Per the GOV.UK Website, you need a UK Standard visitor visa since your Irish visa isn't biometric, because in the eyes of the UK, you aren't actually in transit, as they treat the Common Travel Area as a single country (Ireland doesn't share this viewpoint though).
If you were in transit to outside the Common Travel Area, your green card would be enough, both for airside and landside transit. But you're going to Ireland, so this doesn't apply (because again, transit to Ireland does not count as transit)
On the other hand, as an Indian you wouldn't have needed an Irish visa in addition, as the UK visa lets you enter Ireland for a stay of max 3 months.