Pretty sure LHR-LPA will be operated by I2 (Iberia Express). My recollection is that they don't have the fold-down tables in the middle seat as with BA (I2 is in the process of changing seats, so what you get will vary). Don't know how the crew would react to putting the infant in the middle seat after takeoff.
As to the prices, very difficult to say whether revenue management would increase he number of seats in the cheaper fare buckets. It's a fairly popular leisure destination from the U.K., albeit that September is not the highest season.