Is there a connection between "ivrit" and "livrit" or is there a connection between the word for hebrew language and the word for covenant?

לִבְרִית (livrit) is the noun בְּרִית (b(ə)rit) 'covenant, alliance' with the preposition לִ (l-) 'to, for', so לִבְרִית (livrit) means 'to/for covenant, to/for alliance' and corresponds to the English 'for an everlasting covenant' in King James Version Gen. 17:7. The letter ב is pronounced as [b] at the beginning of the word and as [v] inside the word. The [b] reading is marked with a dagesh, a dot inside the letter בּ in the word b(ə)rit.

The word עִבְרִית‎ (ivrit) comes from עֵבֶר‎ (ʻéver) 'Eber', the ancestor of the Israelites. Probably related to עָבַר‎ (ʻavár, “to cross”), from the crossing of the river Euphrates or Jordan to Canaan. עֵבֶר‎ (ʻéver) 'Eber' has the root ע־ב־ר‎ (ʻ-b-r) meaning 'to pass, to cross'.

In Hebrew, as it is usual in a Semitic language, the root of the verb consists of consonants only, vowels are inserted between those consonants to make different forms of the word. Since in בְּרִית (b(ə)rit) the first root consonant is ב (b) and in עִבְרִית (ivrit) the first root consonant is ע (ʻ) – that is a pharyngeal Semitic consonant which is not pronounced now by most Modern Hebrew speakers, – we see that the two words have different roots, so they are not related.