Intensity fluctuations in lasers are commonly studied above threshold in some special configurations (especially when emission is fed back into the cavity or when two lasers are coupled) and related with their chaotic behaviour. Similar fluctuating instabilities are usually observed in random lasers, which are open systems with plenty of quasi-modes whose non orthogonality enables them to exchange energy and provides the sort of loss mechanism whose interplay with pumping leads to replica symmetry breaking. The latter however, had never been observed in plain cavity lasers where disorder is absent or not intentionally added. Here we show a fluctuating lasing behaviour at the lasing threshold both in solid and liquid dye lasers. Above and below a narrow range around the threshold the spectral line-shape is well correlated with the pump energy. At the threshold such correlation disappears, and the system enters a regime where emitted laser fluctuates between narrow, intense and broad, weak peaks. The immense number of modes and the reduced resonator quality favour the coupling of modes and prepares the system so that replica symmetry breaking occurs without added disorder.