Lace-webbed Spider is a name given to (at least) two common species of house spiders of the genus Amaurobius: Amaurobius similis and Amaurobius fenestralis.
They vary in body size from 7 mm to 12 mm, with large, strong legs.
They are noctunal.
The specific name similis is based on its similarity to the species Amaurobius fenestralis.
Both are often found near windows, hence the specific name of Amaurobius fenestralis.
The two species are difficult to distinguish: An adult Amaurobius similis tends to be larger and darker in colouration and prefers the indoors.
Both species have V-shaped markings on their abdomens, with Amaurobius similis usually having four, and Amaurobius fenestralis two or three.
However, the two species have a different tibial apophysis (some sort of "shinbone") connected to the pedipalps (the two "antennae" in front of the spider which function as taste and smell organs). The 3rd photo shows this tibial apophysis (as a little "hook") and its shape is typical for Amaurobius similis.

An adult male. Madeira, Portugal, 9 November 2013