The article that describes this research does discuss their favored model for explaining these features. The article starts off by talking about Earth analogues, which are always helpful. In this case, it talks about brines rising in antarctic ice shelves (brines being just what they are in cooking -- salty water, and salt lowers the freezing point of water by up to and over 10°C).
The model the authors suggest starts with a thermal plume that heads from the liquid interior up through the ice and melts some of the overlying ice. The melting causes the surface to collapse a bit and fracture (volume of water is < volume of ice), and this confines the water to that region. The thermal plume was transient/temporary and sinks back down, and the water at the base of the "lake" re-freezes. The article then talks a lot about the morphology (what it looks like) in images and theory, showing that the two intersect.
As the lens of water lies below the surface, the surface fractures and calves, like glaciers calving on Earth. Material fills in with an impurity-rich matrix and freezes. When the lake underneath refreezes, since the volume of the ice is greater than water, it creates a positive convex topographic relief (jumbled because of the previously calved blocks) as opposed to the concave one when there was liquid below.
From what I can tell, the article is not actually suggesting that all these areas presently contain liquid water lakes underneath them. They do suggest one particular area, Thera Macula, to be presently active, however. Their argument for this is based on its morphology: "The large concentric fracture system encircling Thera Macula resembles those of collapsing ice cauldrons, and, given the absence of a continuous moat, suggests that subsurface melt and ice disaggregation is forming Thera Macula, rather than the collapse of a dome."
They suggest, "Today, a melt lens of 20,000–60,000 km3 of liquid water probably lies below Thera Macula; this equates to at least the estimated combined volume of the Great Lakes." The timescale for this amount of liquid to re-freeze is 100,000-1,000,000 years.
The type of terrain that this creates ("chaos terrain") is spread throughout the moon, so if their model is correct, then it has had many intra-ice lakes throughout its history, and likely throughout its recent history. The authors conclude with, "Our analyses suggest that ice–water dynamics are active today on Europa, sustaining large liquid lakes perched in the shallow subsurface."