No, lavender is not very amenable to pruning except to remove spent flowers (an aesthetic choice, not one which really impacts plant health or growth) and any dead branches that might appear (we don't see any in the photo). Like its cousin rosemary, lavender is more like a shrub than an herbaceous perennial; it is generally not pruned back drastically since it will not regrow well from such treatment. As the plant ages, the lowermost and innermost foliage can wither/blacken and fall off (though sometimes it doesn't shed right away, so dead leaves can be left hanging on the stems), which is perfectly normal. The live growth on the branch tips tends to hide most of that, at least on full, healthy plants; another reason to avoid trimming branches back too far. You might be able to carefully brush those dead leaves off by hand if you prefer a cleaner look, but otherwise the branches tend to be fairly brittle and easy to break when attempting that, so most lavender growers just leave them as-is.

Miri