What does “falls into clover with a lock” mean?
Solution 1:
To be in clover is to enjoy prosperous circumstances, through effort and/or luck. (I believe the writer's use of "fall" in this case emphasizes luck over effort.)
To have a lock on something is to own or control it completely. Part of the connotation is to deny (lock out) someone else's efforts to control the thing.
Here, "with a lock" is not part of the idiom "falls into clover." Rephrased: "With a lock on the White House and both houses of Congress, the G.O.P. falls into clover ..."