My car will stay running

When I start my car, 1999 Lexus RX-300,it will cut off immediately. I checked electrical connections and things seem tight.If I keep my foot on gas pedal car continue to run but when I take it off it stops.

When an engine stalls out as soon as the accelerator is released, it usually points to a dirty/malfunctioning Idle Air Control valve.

You can try removing the IAC valve and cleaning it and the idle air bleed port on the throttle body to see if that remedies the problem. If not, then the IAC valve may require replacement.