In phenomenology, the lived body is your own body as experienced by yourself, as yourself. Your own body manifests itself to you mainly as your possibilities of acting in the world. It is what lets you reach out and grab something, for instance, but it also, and more importantly, allows for the possibility of changing your point of view. This helps you differentiate one thing from another by the experience of moving around it, seeing new aspects of it (often referred to as making the absent present and the present absent), and still retaining the notion that this is the same thing that you saw other aspects of just a moment ago (it is identical). Your body is also experienced as a duality, both as object (you can touch your own hand) and as your own subjectivity (you are being touched).
Empathy refers to the experience of another human body as another subjectivity: In one sense, you see another body, but what you immediately perceive or experience is another subject. In Husserl's original account, this was done by a sort of apperception built on the experiences of your own lived-body.
The experience of your own body as your own subjectivity is then applied to the experience of another's body, which, through apperception, is constituted as another subjectivity. You can thus recognise the Other's intentions, emotions, etc. This experience of empathy is important in the phenomenological account of intersubjectivity. In phenomenology, intersubjectivity is what constitutes objectivity (i.e., what you experience as objective is experienced as being intersubjectively available - available to all other subjects. This does not imply that objectivity is reduced to subjectivity nor does it imply a relativist position, cf. for instance intersubjective verifiability).
In the experience of intersubjectivity, one also experiences oneself as being a subject among other subjects, and one experiences oneself as existing objectively for these Others; one experiences oneself as the noema of Others' noeses, or as a subject in another's empathic experience. As such, one experiences oneself as objectively existing subjectivity. Intersubjectivity is also a part in the constitution of one's lifeworld, especially as "homeworld."