L30 TRACON Controller reported the adjacent sector had to vector a departing aircraft to avoid a conflict with two arriving aircraft. The reporter states the published arrival and departure procedures are unsafe and do not ensure separation between aircraft.

Narrative

Vectors off the RNAV arrivals were necessary for sequencing. This is not uncommon due to traffic volume. The speeds altitudes at the outer fixes are 280 knots 19000 feet to 14;000feet (Arrival window) for RKSTR arrivals and 250 knots and 19;000 feet for CHOWW arrival. Getting Aircraft X and Aircraft Y to descend became an issue due to their speeds of 280 knots or greater. They of course couldn't get below 10;000 feet until slowing to 250 knots. Both aircraft were on vectors to intercept the localizer outside the Initial Approach Fix of PRINO. Crossing altitude for PRINO is 8;000 feet. I observed Aircraft Z on the NIITZ departure converging toward Aircraft X and Aircraft Y. The last restriction for the NIITZ departure is OLBLU 10;000 feet and 250 knots. This departure crosses over the Runway 26L localizer about 9 miles outside of PRINO. This is where Aircraft X and Aircraft Y were being sequenced to. I called MED departure sector and instructed them to turn Aircraft Z left to avoid a loss or even a near midair collision. The Departure Controller turned Aircraft Z in time and IFR separation was maintained. MED departure sector has [approval] to climb through LAK arrival sector.The outer fixes of RKSTR and CHOWW need to be lowered to at least 17;000 feet. Also; the speeds must be 250 knots. This would allow the departures to climb over the arrivals. As it is now; we are accepting arrivals at 19;000 feet and departing with an altitude of 19;000 feet. The arrival and departure tracks cross. Also; the NIITZ departure requires another fix beyond OLBLU to force aircraft to climb above the arrivals. This new fix should have an altitude of at least 15;000 feet and the speed of 250 knots. The NIITZ departure as published now. Allows aircraft to accelerate faster than 250 knots after OLBLU. This equates to an aircraft accelerating at 10;000 feet instead of climbing faster.