I don't have anything for this season, but the L.A. Clippers made the most free throws by a team in the 2021 playoffs, with 371 made.

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teams with most free throws this playoffs
ClippersSunsBucksHawks76ersJazzNetsNuggetsTrail BlazersLakersCelticsWizardsMavericksKnicksGrizzliesHeat37135234330024121421115911611411310999898162
TEAMGPFTMMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTAFT%MINPTSREBASTSTLBLKTOVPF
L.A. ClippersL.A. Clippers19371240.0111.641.220.86.84.310.739.181.947.713.836.438.123.782.34,5602,12078239512981203370
Phoenix SunsPhoenix Suns22352240.0109.042.723.26.54.211.940.985.048.111.229.737.618.686.15,2802,39893951114292262434
Milwaukee BucksMilwaukee Bucks23343242.2110.349.022.87.84.212.742.191.146.211.235.032.120.871.85,5702,5371,12652518097293413
Atlanta HawksAtlanta Hawks18300240.0106.342.420.26.74.412.438.986.844.911.734.234.320.979.84,3201,91376336412179224382
Philadelphia 76ersPhiladelphia 76ers12241240.0116.344.724.98.06.212.842.585.849.611.228.439.329.368.52,8801,3955362999674154276
Utah JazzUtah Jazz11214240.0116.942.419.65.24.113.539.784.247.218.043.641.324.380.12,6401,2864662165745148237
Brooklyn NetsBrooklyn Nets12211242.1112.542.622.67.14.811.640.786.247.213.635.638.220.386.82,9051,3505112718558139254
Denver NuggetsDenver Nuggets10159245.0114.843.624.96.14.311.242.192.245.714.738.538.220.976.12,4501,1484362496143112204
Portland Trail BlazersPortland Trail Blazers6116248.3119.541.722.85.25.511.842.088.347.516.239.241.322.785.31,490717250137313371139
Los Angeles LakersLos Angeles Lakers6114240.097.543.219.36.74.013.834.383.041.49.832.829.924.577.61,440585259116402483123
Boston CelticsBoston Celtics5113240.0112.241.421.06.47.013.038.488.243.512.836.635.027.482.51,200561207105323565105
Washington WizardsWashington Wizards5109240.0110.043.422.44.84.813.440.688.645.87.024.228.929.075.21,200550217112242467120
Dallas MavericksDallas Mavericks799240.0106.040.620.75.62.111.039.186.045.513.635.038.820.070.71,680742284145391577142
New York KnicksNew York Knicks589240.097.046.418.65.82.812.234.486.439.810.430.434.221.881.71,2004852329329146199
Memphis GrizzliesMemphis Grizzlies581240.0115.041.222.08.04.010.444.294.446.810.431.632.920.479.41,200575206110402052103
Miami HeatMiami Heat462246.398.042.321.57.33.514.035.389.339.512.035.833.620.376.59853921698629145682