The debugger uses ^C for interrupting the target, so it assumes that you don't actually want the ^C propagated to the target. You can change this behavior by using the "process handle" command:
(lldb) process handle SIGINT -p true
telling lldb to "pass" SIGINT to the process.
If you had stopped the process in lldb by issuing a ^C, then when you change the process handle
as shown here and continue, that SIGINT will be forwarded to the process.
If you stopped for some other reason, after specifying SIGINT to be passed to the process, you can generate a SIGINT by getting the PID of the debugee using the process status
and send a SIGINT directly to said process using platform shell:
(lldb) process status
(lldb) platform shell kill -INT {{PID from previous step}}
(lldb) continue
process handle SIGINT -s false
. – Seminarian