Basically, lovage needs the following optimal growing conditions:
It grows vigorously. This means that the soil needs to be rich in nutrients and not too dry. Your best option would be sandy loam, for example.
Its roots are strong and reach deep into the ground, so the soil should be deep and loose.
If it is fully exposed to direct sunlight, lovage can only grow if the ground and moisture conditions are correct — otherwise it gets too hot. Areas that are partially or occasionally shaded are ideal.
I have experienced the same problems you are having, which was due to the soil being too dry and low in nutrients (especially in sandy soil with no humus or when using poor-quality soil in plant pots), or if the soil is too heavily compressed and/or too wet (especially in clay soil).
Try growing your lovage again; this time in a semi-shaded part of your garden with the soil conditions described above — deep, loose and enriched with compost. In the right conditions, your lovage should thrive!