I have not tried it, but here is the latest news from Roblox: [Beta] Transfer Experiences to Groups & Track Group Activity
Currently, Studio Lite can only publish to public experiences on your profile. So, once you transfer it, you will need a new public experience in your profile for Studio Lite to publish to.
EDIT: Studio Lite can now publish to Group owned games and to Private games. See the last paragraph of Tip#1 above.