From the TTT EE Appendices we know that the two first lines of Éowyn's dirge are:
Bealocwealm hafað fréone frecan forth onsended
giedd sculon singan gléomenn sorgiende on Meduselde...
'An evil death has set forth the noble warrior
A song shall sing sorrowing minstrels in Meduseld...'
What is interesting here the first line is very similar to a line from Beowulf (line 2265): Bealocwelm hafað fela feorhcynna forð onsended... 'Baleful death has many of my living kin sent forth...' (thanks to Pernilla Jansson from Sweden). David Salo, author of Éowyn's dirge, wanted another parallel between Old English poetical tradition and the culture of the Rohirrim. It is very beautiful!