| I love thee to the depth and breadth and height |
The kind of love described in this passage almost sounds more like admiration and esteem – loving someone to the greatest "height" that your soul can go.
| I love thee with a love I seemed to lose |
The speaker's love for "thee" is the kind of love she had for her childhood heroes and other people she admired. Either she has lost these people because they died, or she's been disillusioned about them.