The reason why anything is ever considered a substitute for normal salt (NaCl) is that some people take too much salt with their diet and this is widely thought to be bad for your blood pressure. This, however, is disputed by some mainly on the grounds that only a small proportion of people are sensitive to hight sodium in the diet and the rest of us can cope with widely differing amounts with no discernible harm.
However, this doesn't mean that anything that tastes like salt is necessarily a good substitute. Not having enough salt is also a problem as the Na/K balance in cells is important and a serious lack of sodium can be an acute danger. For most people with an adequate diet, using a salt substitute (for table salt) can reduce their sodium intake but, since there is already a lot of sodium in the diet, won't cause a problem. But not for all people.
The most common table salt substitute is KCl, which, again, won't be harmful to people with a normal diet. The body is good at processing potassium and sodium and can regulate their levels within reasonable bounds. So KCl is safe as the body is used to coping with it.
This isn't true for lithium. There is no major biological role for lithium in the body, and, while lithium is regarded as an essential trace element, nobody really knows why. Whatever the normal role, the body is not designed to cope with significant amounts of it (unlike K and Na which are major components of many biological systems). So this might suggest that using large amounts a salt substitute has an unknown risk for harm far greater than the use of, say, potassium. Moreover, lithium does has significant known effects on the nervous system, though the mechanisms are poorly understood. This is illustrated by the use of controlled amounts of lithium salts as a significant treatment for bipolar disorder. This fact alone (regardless of any other toxic effects in high doses) would suggest it isn't a safe alternative when used as a substitute for table salt in uncontrolled doses.
The use of lithium as a treatment for bipolar disorder is relatively recent (started in the early 1950s) so it might have looked like a harmless alternative to sodium chloride in earlier times.