i am not an expert on the oil systems of e30's but i'm going to give you my best guess at the situation...
First a question, when and what did you do (if anything) to the car right before you had this happening to you? when is the last time you changed your oil / filter?
If i were you i would look into the oil filter and double check that all the gaskets are in their proper places to insure a good seal of the entire compartment. If the lubrication of the start up relies on pressure built up in the oil system then this could be a problem (like i said im not an expert on this system)
Here is a link you can use to find where each gasket is supposed to go: RealOEM.COM * BMW E30 318i LUBRICATION SYSTEM-OIL FILTER
The second part i would look into would be your control valve on your actual oil pump. This valve may me sticking slightly from age and keeping your oil from advancing as it needs to... ( again just a guess)
Placement of the valve: #5 RealOEM.COM * BMW E30 318i LUBRICATION SYSTEM/OIL PUMP WITH DRIVE
The third and I am not even sure if they have this in the e30 is there is a valve in your valve cover (on e36's) which holds the oil in the valve system to keep it lubricated when you need to start it cold... this is known to go bad (which is the cause of valve tick on many bmws) again im not an expert, and havent seen anything that says e30's even have this valve but it may lead you in a more focused direction...