The music for the series was mostly done on synths standing in for orchestra for budget reasons. Still there are plenty of medieval and renaissance style tracks in the score, as well as pure late 80s synths. The opening and ending themes were J-pop of course, but done in a way that actually fit the tone of the series. In most anime you have the perky poppy song as the opening and the more serious song as the end credits, but Record of Lodoss War reversed that. I did my best to find the Japanese song version of the opening track Adesso e Fortuna sung by Sherry. But all I could find was the English dub, not bad, but not great. It was an early dub from CPM and they were all over the place.
I did find a wonderful cover of the instrumental version featuring a piano and cello. Seriously these two pretty much nailed the sound and feel of the version on the CD. So enjoy some fans performing this anime classic.