The two bridges were built around 1880 and carried the Midland Railway (formerly the "Little" North Western Railway) across a long U-shaped bend in the river. The railway line was closed to passengers in 1966, and dismantled in the 1970s. Both bridges are Grade II Listed.
I have seen the bridge design credited to Edmund Sharpe, but there seems to be a discrepancy with dates. English Heritage list the bridges as being in the 1880s, but Sharpe's involvement with the railway line dates from when it was first constructed in the late 1840s. If anyone knows anything more, please post in the comments.
Both bridges are essentially identical, consisting of a number of wrought iron arch spans supported on sandstone masonry piers and abutments. The choice of material may explain the discrepancy in dates. The shape of the arches seems to indicate cast iron, but closer examination shows riveted construction. Perhaps cast iron spans were replaced in wrought iron?
Whatever the case may be, these are fine bridges.
The east bridge was extensively refurbished in 2013 at a cost of between £1m and £1.5m.
Update 4th September 2014:
Correspondent Bill Hosfield provides the following further information:
"The anomalies about the dates of these two bridges is no doubt due to the following facts. These twin bridges were originally built to carry what became known as the "Little North Western Railway" over the Lune, and this officially opened to traffic on the 17th of November, 1849. The connecting of Edmund Sharpe's name with these two bridges is due to the fact that this Lancaster architect was responsible not only for designing the railway but for being the contractor for constructing a section of the line, and finally taking over the running of the company.
"The second date ascribed to these bridges is due to the fact that when built this railway had only a single track but in 1888/9 a second track was added and so to accommodate this the bridges had to be reconstructed. This necessitated the widening the orginal stone piers and replacing what had been timber beams with the present metal arches. From a detailed study of the masonry work it is possible to see where the new work was bonded to the old, and also to see some of the sockets in the stonework that received the ends of the struts that supported the timber beams".Further information: