"Can I turn on the light?"
:/ I know that in English it is "Can I turn-on the light?", but we are talking about Chinese here.
The correct use of 把 is: Object (action) + 把 + object (recipient of action) + verb + (other).
把 has a clear directional meaning of going from the object of action to its recipient object.
Now, look at your sentence: 可以把开灯吗？The object of action is yourself, the recipient object should be the light, however, the verb 开, which comes right after 把, is now the recipient, but a verb is the action itself and not the recipient of an action.
The correct sentence should be: （我）可以把灯打开吗？
（我）object of action + 把 + 灯 recipient of action + 打开 verb