swift-corelibs-xctest uses the LLVM lit test runner to compile test cases and run them. The Swift build script, utils/build-script, does the same. The Swift build script already contains logic to find a lit executable. XCTest should use the same lit executable.
XCTest's build_script.py has a "test" subcommand that takes a "--lit" path argument (added in https://github.com/apple/swift-corelibs-xctest/pull/76). A modification should be made to the Swift build script to pass something like the following to the Linux XCTest build: https://github.com/apple/swift/blob/723559526475551de6c8211961c7f355279b85ef/utils/build-script-impl#L1763.
Here's where the Linux tests for XCTest are kicked off: https://github.com/apple/swift/blob/e8eba770d58ce512046951b0647941194987525e/utils/build-script-impl#L2203