As one who has worked alongside Word Alone, and greatly respects Sola Publishing and uses their materials, I will say it here first: these are hardly unbiased organizations when it comes to discussing, let alone critiquing, the ELCA.
The ELCA needs critiquing. But the LCMS does also. And here I will critique one statement from the website that intends to explain what the LCMS does with the doctrine of the Holy Trinity:
"LCMS – The LCMS believes in the Triune God. “On the basis of the Holy Scriptures we teach the sublime article of the Holy Trinity; that is, we teach that the one true God, Deut. 6:4; 1 Cor. 8:4, is the Father and the Son and the Holy Ghost, three distinct persons, but of one and the same divine essence, equal in power, equal in eternity, equal in majesty, because each person possesses the one divine essence entire, Col. 2:9, Matt. 28:19."
My critique: The LCMS confesses the Triune God, and it most certainly does teach "the sublime article of the Holy Trinity." But the LCMS cannot believe in the Triune God. As a church body, its leaders and those in its congregations can only pray that those belonging to the LCMS faithfully believe in the Triune God, in the same way that I as an ELCA pastor pray that all those in the ELCA believe in the Triune God and confess the doctrine of the Holy Trinity as confessed by the one holy catholic and apostolic church. There are those individuals and yes, congregations with notorious websites in the ELCA which sadly and sometimes scandalously do not believe and confess this truth. However, I will remind the readers here, gently, that within the LCMS there has been, and may still be, quite vigorous discussion and disagreement regarding certain aspects of the doctrine of the Holy Trinity, especially regarding the possible subordination of the 2nd Person of the Trinity to the 1st Person, that has erupted among theologians, teachers, and pastors in the LCMS in their discussions on the role of women as leaders in the church. And the website of "herchurch" while scandalous is still not a replacement for the statement of faith in the Constitution of the ELCA, which speaks officially for the teaching of the ELCA on this matter just as the material cited for the LCMS on this website is how the LCMS officially speaks for what it confesses as a denomination.
And I will say that, as an ELCA pastor, I confess and teach the doctrine of the Holy Trinity. But I believe in the God revealed in Holy Scripture, which witnesses to the truth of that doctrine as formulated through the councils of the Church. And one more small critique (this time of what is quoted from the ELCA website, most of what I think is a good statement): I can trust in the Father, Son and Holy Spirit; and I can pray for an obedient heart and try to obey Him. But sadly, no, I cannot "just do it." (Meaning, worship and obey God.) Mea culpa. Nor can any of us, which is why we need a savior.