Try thism breaks the line so no gap required. Can set radius if required set to 4 at moment.
; Break p/lines at intersection
; By AlanH April 2023
(defun c:wow ( / ss1 ss2 rad obj2 intpt obj intpts pt1 pt2 )
(setq oldsnap (getvar 'osmode))
(prompt "Select cut line ")
(setq ss1 (ssget "_+.:E:S" '((0 . "LWPOLYLINE,LINE"))))
(princ "\n")
(prompt "Select break line ")
(setq ss2 (ssget "_+.:E:S" '((0 . "LWPOLYLINE,LINE"))))
(setvar 'osmode 0)
(setq rad 4)
(repeat (setq x (sslength ss1))
(setq obj1 (vlax-ename->vla-object (ssname ss1 (setq x (- x 1)))))
(repeat (setq y (sslength ss2))
(setq obj2 (vlax-ename->vla-object (ssname ss2 (setq y (- y 1)))))
(setq intpt (vlax-invoke obj2 'intersectWith obj1 acExtendThisEntity))
(if intpt
(progn
(command "circle" intpt rad)
(setq obj (vlax-ename->vla-object (entlast)))
(setq intpts (vlax-invoke obj2 'intersectWith obj acExtendThisEntity))
(entdel (entlast))
(setq pt1 (list (car intpts)(cadr intpts)))
(setq pt2 (list (nth 3 intpts)(nth 4 intpts)))
(command "break" pt1 pt2)
(command "arc" "S" pt1 "E" pt2 "R" rad)
)
)
)
)
(setvar 'osmode oldsnap)
(princ)
)
(c:wow)