Looking at the numbers and comparing to JPL Horizons, the best match is to the position of the Earth-Moon Barycenter in heliocentric coordinates. That's of course consistent with the data being labeled as: EMB, Ecliptic Heliocentric Coordinates.
If you can live with some small uncertainties due to the details of how coordinate transforms may evolve over time, I believe you can just apply some simple trigonometry. You can confirm here.
$$r = \sqrt{x^2 + y^2 + z^2}$$
$$l = tan^{-1}(y/x)$$
$$b = sin^{-1}(z/r)$$
Data in Question: for JD 2415021.0
position (AU): [-0.2054467990, 0.9615310525, 0.0002141233]
velocity (AU/day): [-0.0171063024, -0.0036576954, -0.0000011815]
JPL Horizions Earth-Moon barycenter J2000 Heliocentric for JD 2415021.0
position (AU): [-0.2054465857, 0.9615310983, 0.00021393097]
velocity (AU/day): [-0.0171063032, -0.0036576916, -0.00000118253]
JPL Horizions Earth J2000 Heliocentric for JD 2415021.0
position (AU): [-0.2054522688, 0.9615603123, 0.00021303115]
velocity (AU/day): [-0.0171136285, -0.0036594066, -0.00000182603]
JPL Horizions Earth J2000 Solar System barycenter for JD 2415021.0
position (AU): [-0.2022720210, 0.9679285296, 0.00010939456]
velocity (AU/day): [-0.0171209826, -0.0036556277, -0.00000165111]