  Our aim was to determine the initial Li content of two clusters of similar
metallicity but very different ages, the old open cluster NGC 2243 and the
metal-rich globular cluster NGC 104. We compared the lithium abundances derived
for a large sample of stars (from the turn-off to the red giant branch) in each
cluster. For NGC 2243 the Li abundances are from the catalogues released by the
Gaia-ESO Public Spectroscopic Survey, while for NGC 104 we measured the Li
abundance using FLAMES/GIRAFFE spectra, which include archival data and new
observations. We took the initial Li of NGC 2243 to be the lithium measured in
stars on the hot side of the Li dip. We used the difference between the initial
abundances and the post first dredge-up Li values of NGC 2243, and by adding
this amount to the post first dredge-up stars of NGC~104 we were able to infer
the initial Li of this cluster. Moreover, we compared our observational results
to the predictions of theoretical stellar models for the difference between the
initial Li abundance and that after the first dredge-up. The initial lithium
content of NGC 2243 was found to be A(Li)_i = 2.85dex by taking the average Li
abundance measured from the five hottest stars with the highest lithium
abundance. This value is 1.69 dex higher than the lithium abundance derived in
post first dredge-up stars. By adding this number to the lithium abundance
derived in the post first dredge-up stars in NGC~104, we infer a lower limit of
its initial lithium content of A(Li)_i= 2.30dex. Stellar models predict similar
values. Therefore, our result offers important insights for further theoretical
developments.
