You need to tell us what sort of carburettors your car is fitted with, Linda, as the starting procedures are different.
WEBER/DELLORTO CARBURETTORS
Identifiable by 4 separate inlet runners coming out of the cylinder head on the right hand side. Also, the carburettors (bolted to these runners on the right hand side of the engine) will have 'Weber' or 'Dellorto' cast into them somewhere on top!
If the car is on Webers or Dellorto's, you shouldn't need the choke to start from
cold unless it is
really cold. Normally, a couple of pumps on the throttle, then turn the key and it should fire. you may need to blip the throttle for a few seconds before it will idle happily and it is good practice to let it warm for a couple of minutes before driving off, otherwise it will tend to cough and sneeze a bit at first.
When starting from
hot on Webers, you should not depress the throttle, as it is easy to 'flood' the engine. If the engine fails to start, depress the throttle slightly, but release it when the engine fires. If you have real problems starting (ie. if you have flooded it) press the throttle pedal all the way to the floor and hold it there - do not pump!! - turn the key and let the engine crank with the throttle full open until it fire, then release the throttle immediately.
STROMBERG CARBURETTORS
These can be identified by two 'Y' shaped inlet runners on the right hand side of the engine - ie. four outlets from the engine merging to two where they connect to the carburettors. Also, the carburettors have domed tops, a bit reminiscent of the 'onion' domes on Russian churches.
Contrary to Jason's advice (which I assume was intended to apply to Weber or Dellorto equipped cars), you probably will need a bit of choke to start a Stromberg car from
cold.
There is absolutely no point pumping the throttle on a Stromberg, 'cos they don't have accelerator pumps!
Stromberg equipped cars can be a bit difficult to start when
hot. If the engine doesn't start when you turn the key, press the throttle pedal all the way to the floor and hold it there while operating the starter; release the throttle as soon as the engine starts
TRAFFIC MANNERS
The cutting out on prolonged idling and stalling in traffic is
not normal for a Lotus Twin Cam engine in good health and tune - they are noted for their tractability and good manners when they are correctly set up.
Stromberg carburettors have a habit of icing up under prolonged high-speed running (particularly in cool, damp weather), so the engine may die if, for instance, you have been running at high speed then come to a halt at a junction. If this happens, leave the car for a few minutes and the heat soak from the engine will melt the ice and the engine should start and run fine.
You will probably need an expert to cure your running problems, unfortunately, so I won't bother going into diagnostics here unless you want me to...your best bet is to get the car to a reputable tuner of 'classic' carburettor equipped cars.