The only free and comprehensive online etymological dictionary of the Spanish language
línea f. (Noun) "line"
13th cent. Old Spanish liña. From Latin linea 'id.,' literally "line of thread." From lineus "flaxen," from linum "flax." From Proto-Italic *līno- 'id.' The variation between *lino- and *linto- means this is probably a loanword from a non-Indo-European language.
Asturian llinia, Portuguese linha, Catalan línia, French ligne, Italian linea, Romanian linie
Latin linteum "cloth," "sail," linteō "weaver" (< Proto-Italic *linto)
Old Prussian lynno "flax," Lithuanian lìnas 'id.,' Latvian lini 'id.," lьnъ "flax," Russian lën "flax," Czech len "flax," Polish len 'id.,' Slovene lȃn "flax"
Ancient Greek λίνον (línon) "linen," Mycenaean ri-no 'id.'

"[An Indo-European] word for 'flax' (*linom) is confined to ... northwest Europe (Celtic, Italic, Baltic, Slavic, possibly Germanic) and Greece. Flax (Linum usitatissimum) was domesticated quite early in southwest Asia and is found on Neolithic sites at least from central and northern as well as southern Europe but is not recorded until quite late in the regions north of the Black Sea." ~ Mallory & Adams, Encyclopedia of Indo-European Culture (1997)