Proposal:
Add an unmerged-dependencies label, which prevents LGTM'd and otherwise good-to-go PRs from being automatically merged. Alternatively, a more general no-merge label could accomplish the same thing.

Motivation:
There are sometimes PRs which have a dependency on another (unmerged) PR. If the dependency is soft (code runs & tests pass), then there is a risk that if the depending PR is LGTM'd before the dependent PR, it can be submitted first.

Here is an example of this happening: kubernetes/kubernetes#17548

/cc @erictune