“lawsuit.” The Hebrew noun translated “lawsuit” is rib (#07379 רִיב pronounced reeb, related to the verb, #07378), and it has a wide range of meanings including strife, controversy, dispute, quarrel, accusation, lawsuit, etc. The wide range of meanings is attested to by the different translations in the English versions: “controversy” (ASV, ESV, KJV); “cause against” (BBE); “grievance against” (CJB); “case against” (HCSB, NASB); “enter into judgment with” (Darby); “dispute” (NAB); “charge to bring against” (NIV); “indicts” (NJB); “has an indictment against” (NRSV); “brought charges against” (NLT).
The NET uses “covenant lawsuit,” which can be clarifying because the charges in the lawsuit are based upon the covenant that Israel made with God (Exod. 24:3-8; we refer to it as “the Old Covenant”). Israel broke the covenant so God is bringing a lawsuit against Israel which, because of her refusal to repent and return to God, will eventually lead to Him divorcing her and sending her away (Isa. 50:1; Jer. 3:8).
“covenant faithfulness.” The word translated “mercy” is hesed (#02617 חֶסֶד), and it has a very broad range of meanings, including “mercy, faithfulness, goodness, graciousness, etc. It was also the word used when two or more parties had an agreement or covenant, and it expressed the joint obligations of the parties, such as covenant faithfulness, love, loyalty, or obligation. It is used almost 250 times in the Old Testament, often because Israel had failed to keep the covenant they made with God and thus abandoned their obligations and the covenant faithfulness and love they agreed to. That is the case here in Hosea 4:1.
The reason Yahweh had a “covenant lawsuit” against Israel is that they had broken the covenant they made with God (Exod. 24:3-8; we refer to that covenant as “the Old Covenant”). Israel ignored the covenant they made with God and even openly defied it. God compared His covenant with Israel as a marriage, and when Israel broke the covenant and refused to repent, eventually God divorced Israel and sent her away (Isa. 50:1; Jer. 3:8); Israel was captured by the Assyrians and deported from their land (2 Kings 17:6-23). The deportation of Israel was still future when Hosea 4:1 was written.
The range of meanings of hesed in this context makes it hard to agree on the best English translation, and that fact is reflected in the translations: “goodness” (ASV); “faithful love” (CJB, HCSB); “steadfast love” (ESV); “mercy” (KJV); “loyalty” (NAB, NET); “kindness” (NASB, NLT); “love” (NIV). In fact, however, all those things are based on the fact that Israel abandoned the covenant, and thus “covenant faithfulness” seems to catch all the different failures of Israel. God expects people to keep their vows, oaths, promises, and covenants, and it is very serious when they do not and ignore what they said. As God says in Ecclesiastes: “It is better that you should not vow than that you should vow and not pay. (Eccl. 5:5).