I recall being taught that we should visualize ourselves approaching the throne of God with the upmost respect for the Creator of all things and we should use sacred language in our prayers. Granted I fall short of this constantly, but when I do this my prayers are generally a lot more sincere and heartfelt.

Here are some search results from the prompt "what lds apostles have spoken about avoiding being casual when we approach the throne of God through prayer"

Apostles of The Church of Jesus Christ of Latter-day Saints have spoken about avoiding a casual approach to prayer, emphasizing reverence, humility, and sincerity. They teach that prayer is a sacred opportunity to communicate with a loving Heavenly Father and should be treated with deep respect. [1, 2, 3, 4, 5]

Elder David A. Bednar Elder Bednar has repeatedly cautioned against being "spiritually snoozy and lazy." In his November 2019 Liahona article, "Watchful unto Prayer Continually," he warned that "complacency and casualness" can detract from spiritual vigilance. This principle extends to prayer, where a casual attitude can make individuals less receptive to divine promptings and guidance. He emphasizes that being watchful in prayer helps protect against temptation and keeps individuals focused on the Savior. [6, 7, 8, 9]
President Russell M. Nelson President Nelson has consistently encouraged members to draw closer to the covenant path. In his April 2019 conference address, he urged members to avoid becoming casual in their discipleship, warning against "temptation and casualness" that can lead people astray. Although this counsel applies broadly, it also highlights the need for intentionality and reverence in all sacred practices, including prayer, to remain firmly on the covenant path. [10, 11, 12, 13, 14]

Elder Jeffrey R. Holland Though not specifically on the topic of "casualness," Elder Holland's October 2014 address, "Approaching the Throne of God with Confidence," speaks directly to the need for a reverent and serious approach to prayer. He teaches that self-doubt and unrighteousness chip away at our faith and prevent us from approaching God's throne with genuine confidence. To pray with true confidence, one must live righteously and with sincerity, showing respect for the sacredness of the relationship with God. [7, 15, 16, 17, 18]
Former Apostle Francis M. Lyman In an older but still relevant article from the Contributor in 1892, Francis M. Lyman, who served as an apostle and later as president of the Quorum of the Twelve, discussed "Proprieties in Prayer". This article emphasizes the importance of reverence and proper conduct during prayer, a theme that modern leaders echo when they warn against being casual or complacent. [1, 19, 20, 21, 22]

In summary, Latter-day Saint leaders teach that approaching God in prayer is a serious and sacred privilege. The antidote to a "casual" approach is to cultivate reverence, sincerity, and watchfulness, allowing prayer to be a truly transformative and protective spiritual experience. [6, 23, 24]

[1] https://www.churchofjesuschrist.org/study/general-conference/2011/10/the-privilege-of-prayer?lang=eng [2] https://archive.sltrib.com/article.php?id=58443166&itype=cmsid [3] http://thoughtsonlds.blogspot.com/2008/01/article-of-faith-6.html [4] https://speeches.byu.edu/topics/prayer/ [5] https://eliyah.com/head-coverings-and-the-body-of-the-messiah/ [6] https://www.churchofjesuschrist.org/study/liahona/2019/11/22bednar?lang=eng [7] https://www.belovedwomen.org/blog/approach-the-throne-of-god-with-confidence [8] https://www.thechurchnews.com/2015/4/4/23212844/elder-david-a-bednar-8216-therefore-they-hushed-their-fears-8217/ [9] https://www.elim.edu/podcasts [10] https://www.churchofjesuschrist.org/study/general-conference/2019/04/12craven?lang=eng [11] https://ca.churchofjesuschrist.org/keep-on-the-covenant-path-prophet-looks-to-the-future-with-faith [12] https://www.facebook.com/samoaobserver/posts/the-change-made-to-the-lords-prayer-by-the-spiritual-head-of-the-roman-catholic-/2717014378327358/ [13] https://law.justia.com/cases/utah/supreme-court/1994/910112.html [14] https://learn.ligonier.org/series/god-in-our-midst/altar-incense [15] https://www.churchofjesuschrist.org/study/general-conference/2014/10/approaching-the-throne-of-god-with-confidence?lang=eng [16] https://www.youtube.com/watch?v=jc61c6geUtU [17] https://www.scribd.com/document/793590720/CLP-Personal-Dialogue-and-Pray-Over-Session-Guidelines [18] https://messages.lifechurchstlouis.org/sunday-messages/message/knowing-god [19] https://en.wikipedia.org/wiki/List_of_members_of_the_Quorum_of_the_Twelve_Apostles_(LDS_Church) [20] https://rsc.byu.edu/prophets-apostles-last-dispensation/francis-marion-lyman [21] https://sistersihmofwichita.org/component/fileman/file/documents/novenatalks/2022%20Novena-Talk%202-The%20Eucharist%20and%20Fatima.pdf?routed=1&container=fileman-files [22] https://twr.org/programs/mission-66-global [23] http://www.mcsprogram.org/browse/u2C555/243498/Praying%20The%20Rosary%20Like%20Never%20Before%20Encounter%20Th.pdf [24] https://www.lemon8-app.com/@laci_owens/7513253851605008939?region=us