How do you define the two closest line features with a value?
Street = N Main St and Speed Limit is null
Do you create a buffer around N Main St and pick the first two streets that intersect the buffer (where Speed Limit is not null) and use the average of those two?
Do you check to see what streets are connected to N Main St and take the first two that have non null speed limits and average them?
My point being is you may want to run a few different scenarios on paper and see what logic it would take to make it happen. Let's say some how the two 'closest' streets to your Null Speed Limit street are a freeway (70 mph) and a local street (25 mph). Do you really want to assign a 48 mph speed limit to it?
Apply this to whatever linear feature you might have: Null value in pipeline diameter; Null value in kilovolt transmission line, etc...