Remember in this statue she's only in the company of Myau so, by the time of Phantasy Star I, the only moments she had been alone with her cat was after she trade the laconian pot for him (in Motavia) and before saving Odin (in Palma).
Very true... unless of course that 'Termi episode' had happened when she arrived from "Arisaland"; in that case she would be helding her laconian sword (Myau was alive, Odin death and Lutz sleeping). However all sentences from Termi citizens points that she dethroned Lashiec* by force and all that... so very hardly it wouldn't be during Phantasy Star I, when she was alone with Myau. "Alis sword" is not her laconian sword (consequently not Neisword/Elsydeon).
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* - Well, I must also remember that Lashiec may return with the arrival of Noah spaceship** (which brought dark force) and "as long as he exists" lashiec will not be dead. Concluding : If this "Termi's sword" is the laconian sword or not remains a mistery (but I still believe in the first option).
** They will arrive just 8 years after Alis arrived to Algol (from Copto)