What was the lithium concentration in 1940's 7-Up?
Given that the formula was a trade secret and that lithium was removed from the product ~70 years ago, the likelihood of this question being answered by providing a detailed formula seems remote. Note in addition that the formula might have evolved to reduce cost or improve market reception. You might therefore want to settle for an estimate of the upper limit on the lithium citrate concentration, which is relatively easy to provide.

A basic estimate can be made based on (1) the historical limits of sodium concentration in sodas; (2) the current composition of 7-up; and (3) the relative saltiness (taste) of lithium citrate versus sodium. 

First one can attempt to determine what range of sodium concentration makes for a flavorful soda. Here is a quote:


  The amount of sodium in soda varies depending on the type. A well-known brand of cola has 46 milligrams of sodium in a 12-ounce can. The same sized can of root beer has 71 milligrams; a can of lemon-lime soda has 64 milligrams; a 12-ounce can of all-natural soda contains 36 milligrams. These are just examples, and the amounts in particular brands of soda may differ. It's best to check the label of your favorite soda to make sure.


This leads to a range of ~150-200 mg/L sodium concentration. 

Next, consider the current formula for 7-up (in the USA): 


  in 12 fl oz (355 mL):
    40-50 mg  sodium,
    60 mg potassium


The current formula contains ~110-140 mg/L sodium and ~170 mg/L potassium.

Finally, consider the saltiness of lithium citrate versus sodium. Lithium citrate was the salt form of lithium in the 7-up recipe  according to a number of sources including the Wikipedia:


  The soft drink 7Up was originally named "Bib-Label Lithiated Lemon-Lime Soda" when it was formulated in 1929 because it contained lithium citrate. The beverage was a patent medicine marketed as a cure for hangover. Lithium citrate was removed from 7Up in 1948.[Ref 4]


and  this one (which cites Ref 1):


  As to why “7Up,” C.L. Grigg never explained how he came up with the cryptic name. Several theories exist about its origin:
     "7Up was the product of seven ingredients. (Which, in a way, was at least true with regard to the classes of ingredients in that original formulation: sugar, carbonated water, essences of lemon and lime oils, citric acid, sodium citrate, and lithium citrate.)"


Lithium and potassium are among few cations with a salty flavor similar to that of sodium, albeit weaker. Citrate reduces the saltiness further. According to Ref 2, the saltiness of lithium and potassium can be estimated to be ~0.4 and 0.6 that of sodium, repectively, while Ref 3 explains that citrate has an inhibitory effect.    

Consider now the potassium concentration (~170 mg/L) in the current formula of 7-up. Potassium is added as the citrate salt, and could be replaced with the lithium salt with little change in taste perception, according to what is reported on the relative saltiness of the cations and citrate salts. This suggests that if the taste of the beverage has remained reasonably constant since inception, it is not unreasonable to estimate an upper bound of ~200 mg/L in the concentration of lithium citrate (replacing the potassium salt) in the orginal recipe.  

Note this is based entirely on the taste perception and not on any medical implications of consuming lithium at such concentrations. Lithia water (a brand of spring water sold in the USA) contains only ~0.5 mg/L of lithium. For reference, an online medical advice site suggests that a dose for treatment of depression is ~60 mg of lithium daily. So a dose of ~60 mg lithium citrate per serving certainly seems high relative to lithium-rich spring water but is just about a typical clinical dose.  

References


Rodengen, Jeffrey.   The Legend of Dr. Pepper/7Up.   Fort Lauderdale: Write Stuff Syndicate, 1995.   ISBN 0-945903-49-9.
McLaughlin, S., Margolskee, R.F.. The Sense of Taste. American Scientist, 82, 538-545 (1994).
C.M.D. Man. Technological functions of salt in food products. in Reducing Salt in Foods, Woodhead Publishing, 2007. ISBN 978-1-84569-018-2.
Gielen, Marcel; Edward R. T. Tiekink (2005). Metallotherapeutic drugs and metal-based diagnostic agents: The use of metals in medicine. John Wiley and Sons. p. 3. ISBN 0-470-86403-6.