In Sh'mot, 4:24, the text reads, "וַיְהִ֥י בַדֶּ֖רֶךְ בַּמָּל֑וֹן וַיִּפְגְּשֵׁ֣הוּ יְהוָ֔ה וַיְבַקֵּ֖שׁ הֲמִיתֽוֹ׃ " and the English there (from the sefaria.org page, but the Stone chumash concurs) for the final 2 words is "and sought to kill him." Yirmiyahu 26:21 has a similar construction, for which the sefaria.org has "to put him to death." The only other instance of הֲמִיתֽוֹ is in Mishlei 19:18 which reads " וְאֶל־הֲ֝מִית֗וֹ " and is translated as "on his destruction" (removing any active participation in the killing).
But Tehillim 37:32 has the phrase "וּמְבַקֵּשׁ לַ הֲמִיתוֹ" ("seeking to put him to death") and the word with the lamed occurs 5 other times, always meaning "to kill/put to death."
It seems to me that for the word to be translated as an infinitive verb, "to kill", would require the lamed and that appears 6 times. And yet in two cases, the form without the lamed is still translated as that infinitive form.
Are there any commentaries that explore the difference between the form with and without the lamed or which explain how the form without the lamed can still be understood as the active infinitive verb (as opposed to the more passive sense)?