Lovell, 54, says he will be writing to the Utah Supreme Court asking them to intervene.
"Should the Utah Supreme Court choose not to intervene at this time, I an informing this court that co-counsel Sean Young will be the only attorney representing me," Lovell's letter concludes.
Lovell first complained about Bouwhuis in an Aug. 1 letter to Lyon.
At a hearing on Aug. 9, Lovell refused to discuss details of the conflict, but Bouwhuis disclosed that he and Lovell disagreed on the course of action to take after the court in May denied Lovell's request for a new trial judge.
At the August hearing, Lyon ordered Bouwhuis to visit Lovell at the prison to resolve their differences. However, Lovell has continued to write letters to Lyon and the Utah Supreme Court asking for another lead attorney.
In a letter in late August, Lovell wrote to Lyon saying, "[Bouwhuis] does not represent my interests; therefore, my objectives cannot be met. I do not trust him!"
In 1993, Lovell pleaded guilty to murdering Yost in August 1985 to prevent her from testifying against him for raping and kidnapping the woman four months earlier. Lovell said he dumped the woman's body in the mountains east of Ogden.
As part of a plea deal, prosecutors agreed not to pursue the death penalty if Lovell led them to Yost's body.
But after Lovell was unable to find the grave, he was sentenced to death.
In July 2010, however, the Utah Supreme Court ruled Lovell could withdraw the guilty plea because he should have been better informed of his rights by the attorney who represented him previously during court proceedings.
A month-long trial is set to begin Feb. 3 before Lyon.