Overseeding lucerne seeds in an existing lucerne field is absolutely ineffective. The reason behind this is that lucerne plants excrete a chemical substance (Medicarpin) which kills young lucerne seedlings.
The only way to extend production period of a thin stand is to overseed with grasses or clovers. An annual solution is to use Italian ryegrass (15-20 kg/ha) and berseem clover (5-10 kg/ha). For a perennial solution overseeding with NutriFibre tall fescue (25-40 kg/ha) with red clover (5-10 kg/ha) is a great option. Overseeding is ideally done in early spring or autumn, when lucerne growth is slow and there’s time and space for establishment.