As Werther noted in the 2016 melting thread, the Lena Delta is seen clear and beautiful in MODIS today.
Lets compare the Lena River and the Mackenzie River to get some idea of the Lena River and delta potential for sea ice melting.
During the peak month (May) of river discharge, the Mackenzie River averages about 15,000 m3/s discharge. During its peak month (June), The Lena River averages about 80,000 m3/s (
https://epic.awi.de/37164/1/Fedorova_et_al_2015_BG.pdf Fig.2), so about 5 times as much potential heat input as the Mackenzie. Again by comparison with the timing of water appearing at the delta edge on the two deltas, peak discharge at the Lena delta coastline is sometime in the next couple of weeks.
The Lena delta has a much wider area of landfast ice for the discharge water to flow under before it reaches the widening dark ocean. And the Lena delta is almost at a rightangle to the regional Laptev "ice/coast line". But I think we can infer a significant Lena river boost to ice melting in the Laptev Sea during June. (From the discussions of the Mackenzie River input in the 2016 thread, I estimate that at its peak, the Mackenzie River contributed equivalent of about 25% of insolation heat input into the expanding Beaufort polynya. The size of the Lena River implies an even more significant contribution.)
No doubt others can improve these estimates.