Dallas will use the two-week window to negotiate a long-term extension with the pass-rusher. The deadline for using the franchise tag is March 5.
Lawrence was tagged for $17.1 million in 2018 and would cost $20.5 million for 2019. However, he has no desire to play under the franchise tag for a second straight season, according to Hill.
The 26-year-old is widely expected to become the third NFL defender to break the $20-million-per-year mark - joining Khalil Mack and Aaron Donald - after racking up 25 sacks over the last two seasons.
The Cowboys have made it clear that retaining Lawrence is their top priority, and Hill added that they "plan to keep him at all cost."