What are these lines on the nose of a Boeing 737?
I'm no expert on B737 radomes, but I was able to find that these are called Lightning Diversion Strips or Lightning Diverter Strips.

Since radomes are generally built with composites, they do not transmit static electricity in the same way that aluminum skin would.

The B737-200 maintenance manual states that the radome is constructed of fiberglass and is provided with lightning diverter strips on the outside surface—though it states that these are not necessarily provided on all airplanes. It further states that these diverter strips are constructed of thin gauge aluminum.

From b737.org.uk: 


  The radome (RAdar DOME) is an aerodynamic faring that houses the weather radar and ILS localiser and glideslope antennas. Unlike the rest of the fuselage it is made of fibreglass to allow the RF signals through.
  
  Fibreglass is non-conductive which would allow the build up of P-static (static due to the motion of the aircraft through precipitation). This would in turn cause static interference on the antenna within so the radome is fitted with six conductive diverter strips on the outside to dissipate P-static into the airframe.


And from this article:  


  Another important characteristic of the radome is its ability to bleed
  off static electricity. This is done through the use of
  anti-static/anti-erosion coatings and through the lightning diverter
  strips extending from the frontal area of the radome to the airframe.
  "These diverter strips, says Bauer, continuously collect static
  build-up from the surface of the radome and conduct it to the airframe
  without severe sparking or arcing."


Here is a video that explains some of the principles of lighting diversion (note that the particular strips discussed may differ from those found on the B737). The diverter strips are discussed particularly starting here at 2:20: