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Earlier, Madrid were knocked out of the Champions League at the last-16 stage by Ajax Amsterdam.
Madrid are stuck in third on 57 points, 13 behind La Liga leaders Barcelona and five behind city rivals Atletico Madrid.
The victory left Real, who had drawn with Leganes in their last outing, in third place on 64 points.
Real moved on to 60 points after 31 games thanks to the victory but remain third in the standings.
A retractible roof will be built, and the stadium will be wrapped in a titanium facade, while a 360 degree scoreboard will also be installed.
Lampard won 13 trophies in 13 years and became Chelsea's all-time leading marksmen with 211 goals from midfield during a decorated playing career at Stamford Bridge. But he has a lot to prove in his new role.
Bale has won four Champions League titles since joining Madrid from Tottenham Hotspur in 2013 for a then world record 100 million euros.
The French legend clarified that it was the club who wanted to sell the Welsh forward, not him personally.
Real fielded a strong side once again, with new signings Eden Hazard and Luka Jovic starting up front and Gareth Bale again on the bench, but were 5-0 down at the end of a shambolic first half.
Violent protests have been taking place in the region following the imprisonment of nine Catalan political and social leaders for their role in organising an independence referendum in 2017.
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