I am not sure where to look for landholders called Bruce, but if I understand it correctly, this is the meaning behind the "Somehting" Lands? I've seen "Lands" before in Scotland but generally in the ountryside, but that may be more to do with abodes I generally look for.
In a mediaeval town, the street plan is usually a single street, widening in the middle to make space for the church and market. On both sides of the street there are houses, each one with a strip of ground behind it at right angles to the main street. Usually there is a lane or alley along each strip, or perhaps every pair of strips. Over time, the strips of ground get built on as demand for housing in the town increases, and the result is a narrow lane or alley with houses, sometimes several storeys high, on both sides of it. Sometimes the lane or alley is a dead end, and sometimes it has an exit at the other end. The word 'land' is applied to the lane or alley and the houses reached by it.
The Old Town of Edinburgh is a classic example of a mediaeval street layout - take a look at
http://maps.nls.uk/view/74400026 - you will need to zoom in to see it at its best.
You can see a similar plan, albeit the main street layout is a little more complex, of Dundee
http://maps.nls.uk/view/120816545 and there are lots more old street maps on the NLS web site.
In larger cities there can be many streets with lands along them, and the lands acquired names so that they could be distinguished from their neighbours.
A land can be named after the proprietor, or after a tenant-in-chief who rents the whole land from a landlord and lets the individual dwellings in it, or even after a prominent person who is the tenant of one dwelling in the land.
Here's another one - again you'll need to zoom in - showing Miller's Wynd, Mid Wynd and West Wynd.
http://maps.nls.uk/view/74478928 all linking Perth Road and Hawkhill.