We calculate the production rate of the Higgs boson at the LHC in the context of general 5 dimensional (5D) warped scenarios with spacetime background modified from the usual $AdS_5$, and where all the SM fields, including the Higgs, propagate in the bulk. This modification can alleviate considerably the bounds coming from precision electroweak tests and flavor physics. We evaluate the Higgs production rate and show that it is generically consistent with the current experimental results from the LHC for Kaluza-Klein (KK) masses as low as 2 TeV, unlike in pure $AdS_5$ scenarios, where for the same masses, the Higgs production typically receives corrections too large to be consistent with LHC data. Thus the new pressure on warped models arising from LHC Higgs data is also alleviated in $AdS_5$-modified warped scenarios.