The wiki mentions the conspiracy during the Lysene Spring on several occasions, but I would like to get some opinions on the actual period of the Lysene Spring.
The Worldbook says:
In the end, it was Larra Rogare and her wealthy, ambitious family who helped break the power of the regents and, almost certainly, that of Lord Peake. It was an inadvertent role they played, however, caught up as they were in the Lysene Spring. This was a time when the Rogare Bank waxed greater than the Iron Bank, and so fell prey to the plots to control the king; they were blamed for many more acts than they were actually guilty of. Lord Rowan, then the Hand and one of the last regents, was accused of being complicit in their crimes and was tortured for information. Ser Marston Waters, now somehow Hand of the King in his place (Munkun, the only regent at this time besides Rowan, is reticent to discuss this in the True Telling), dispatched men to seize Lady Larra after having arrested her brothers. But the king and his brother refused to give her up, and were besieged in Maegor’s Holdfast by Waters and his supporters for eighteen days. The conspiracy eventually unraveled as Ser Marston—perhaps recalling his duty—attempted to fulfill his king’s command to arrest those who had falsely implicated the Rogares and Lord Rowan. Waters himself was killed by his own sworn brother, Ser Mervyn Flowers, when he attempted to arrest him.
This seems to imply the conspiracy took place during the Lysene Spring, but I'm hesitant to use this as confirmation since we know this paragraph is just a heavily compressed version of the F&B chapter. So I would rather look to Gyldayn's words:
Even less loved than Larra of Lys were the three brothers who had come with her to King’s Landing. Moredo commanded his sister’s guards, whilst Lotho set about establishing a branch of the Rogare Bank atop Visenya’s Hill. Roggerio, the youngest, opened an opulent Lysene pillow house called the Mermaid beside the River Gate, [...] In Lys, ancient houses fell and many a highborn magister was cast down and ruined, whilst others rose up to seize the reins of power. Chief amongst these was Lysandro Rogare and his brother Drazenko, architect of the Dornish alliance. Drazenko’s ties to Sunspear and Lysandro’s to the Iron Throne made the Rogares the princes of Lys in all but name. By the end of 134 AC, some feared they might soon rule Westeros as well. [...] Munkun refers to this period as the Rogare Ascendency, but that term was only ever used at Oldtown, amongst the maesters and archmaesters of the Citadel. The people who lived through it called it the Lysene Spring…for spring was indeed a part of it. Early in 135 AC, the Conclave sent forth its white ravens from Oldtown to herald the end of one of the longest and cruelest winters that the Seven Kingdoms had ever known.
The Rogare Ascendency started in 134 AC, and I guess the Lysene Spring is meant to refer to the same events, although it hadn't been spring when it began. While the term may be a bit imprecise, I think we can deduce the Lysene Spring began late in 134 AC. But when did it end? The last mention of it is this one:
Even as the fighting in the Vale of Arryn continued, the promise of the Lysene Spring suffered another grievous blow hundreds of leagues to the south, with the near-simultaneous demise of Lysandro the Magnificent in Lys and his brother Drazenko in Sunspear.
Since the decline of the Rogares started immediately thereafter, does this mean the death of Lysandro and Drazenko marked the end of the Rogare Ascendency (and if so, does it also mark the end of the Lysene Spring)? Maybe one could argue the actual downfall was some time later when the Rogare Bank went bankrupt. But even then the conspiracy didn't really take place during the Lysene Spring, but after it.