Price sets world best in women's weight throw at US Indoors
Price, the 2019 outdoor hammer throw world champion, twice broke the old mark of 25.60 set by fellow American Gwen Berry at the 2017 US meet.
Price, 29, broke Berry's mark with an effort of 25.77m in the third round then shattered her own mark by reaching 26.02 in the fifth round.
Reigning world outdoor hammer throw champion Brooke Andersen was second in 24.97.
Lyles reached the 60m semi-finals by winning his first-round heat in 6.60 seconds.
Lyles, the two-time reigning 200 world champion who took a bronze medal in the event at Tokyo, won the Boston Indoor Grand Prix in a personal best of 6.51 two weeks ago.
He was disqualified for a false start at last week's Millrose Games.
Lyles had the third-best overall time among qualifiers after Brandon Carnes and J.T. Smith went 1-2 in their heat in 6.59.