Make only a specific region of a video blurry
In your Premiere timeline put two copies of the lower third above each other on top of the footage. Right click on the lower copy and choose Adjustment Layer from the context menu. Now it acts as a mask for any filters you apply to it, affecting only the opaque areas. Apply a blur effect to this adjustment layer and the footage below will blur where the lower third is opaque.



Now because adjustment layers use the opacity of the clip to set the strength of the effect you might find the blur won't be very strong where the lower third is semi opaque (this is what it looks like with the top layer turned off):



You can fix this by making a duplicate of your lower third in After Effects with a more opaque background, and using that as your adjustment layer:



And Voila! Your beautiful lower third with bg blur: