This video shows the traditional and best way to repair a lead valley on a roof.
How to repair tile roof valley.
A properly flashed roof valley should have an ice and water shield installed with roofing felt being properly secured over the ice and water.
Start at the upper row of shingles at the upper end of the valley.
Video recorded while doing a tile repair the usual valley repair that leaks when the water run off the valley metal hope you like it.
If the ice and water shield is missing then you will have to remove the shingles on both sides along the valley put ice and water shield in place and re shingle the roof.