I'm not sure if it had happened by late IA. These are 3 samples from SW Germany Hallstatt Celts study that had southern ancestry and using some tool they were able to guestimate their origins to different regions in N Italy
Proxy for IA Ligurians?
Magdalenenberg_Hallstat.AG:MBG016.AG__BC_573__Cov_35.63%,0.130897,0.151314,0.039598,0.003553,0.050471,-0.005578,-0.0094,-0.002769,0.018612,0.045559,-0.001299,0.01169,-0.019623,-0.007432,0.005022,-0.003845,-0.00665,-0.003421,0.014581,-0.005378,-0.001497,-0.001731,-0.005916,-0.007953,0.010777
Proxy for IA Marche?
Magdalenenberg_Hallstat.AG:MBG004.AG__BC_573__Cov_33.87%,0.137726,0.148267,0.035826,-0.002907,0.048317,-0.007809,0.003055,-0.003,0.016566,0.036265,-0.002436,0.013488,-0.026759,-0.00867,-0.00285,0.001591,0.005737,0.006714,0.001006,-0.000375,0.006489,-0.01051,0.002465,-0.003133,-0.000838
Proxy for IA Veneto/Slovenia?
Hochdorf_Hallstat.AG:HOC004_d.AG__BC_515__Cov_22.36%,0.121791,0.147252,0.038089,0.008398,0.043393,0.007251,0.004465,0.009,0.018612,0.037905,-0.004872,0.005695,-0.020069,0.001927,0.005157,-0.010872,-0.004824,0.007095,0.006034,-0.019509,0.000374,0.000124,-0.000246,-0.004699,-0.002395
Additionally I think some other Hallstatt/La Tene samples plot in the general region of what I consider N Italy for that time. Apart from the Verona samples they might not represent locals, but rather locals from regions outside Italy which might harbour IA N-NW Italian ancestry, unless they just have similar ancestry components and that's why they overlap on G25 pca.
Parançot_IA:CGG023704__BC_530__Cov_94.86%,0.124067,0.155376,0.044877,-0.003876,0.052625,-0.009482,0.003995,0.003692,0.024952,0.040639,-0.000487,0.007943,-0.018583,-0.011285,-0.002986,-0.001989,0.007171,0.000507,0.008799,0.005127,0.009234,0.006183,-0.007641,-0.005904,-0.005987
BasRhin_Nordhouse_IA1.SG:NOR4.SG__BC_550__Cov_10.91%,0.12862,0.153345,0.058454,0,0.04647,-0.006414,-0.00376,0.013615,0.02168,0.031162,-0.013641,0.007493,-0.020515,-0.01445,-0.019137,0.006232,0.005607,-0.011402,0.011564,0.004627,0.005865,0.00507,-0.014666,0.008073,-0.001796
KapiteljskaNjiva_EIA.AG:I5691.AG__BC_655__Cov_67.06%,0.130897,0.147252,0.044877,0.008398,0.042777,-0.002789,-0.001175,-0.001385,0.019225,0.030433,0.003085,0.008542,-0.019623,-0.011973,0.003122,-0.003182,-0.000522,0.003674,-0.005531,0.0005,-0.00262,0.005193,-0.001972,0.002892,-0.000958
Picene_SiroloNumana_IA:

PNU76__BC_600__Cov_11.71%,0.124067,0.15436,0.050157,-0.013889,0.046778,0.000837,-0.00094,-0.004154,0.032315,0.030251,0.003248,0.003297,-0.009663,-0.010046,0.004343,-0.008088,-0.013299,0.012035,-0.01169,-0.01038,-0.007736,-0.003462,0.002958,-0.000964,0
Picene_Novilara_IA:

PN24__BC_675__Cov_22.18%,0.119514,0.161469,0.042615,0.002261,0.0437,-0.001394,-0.00517,0,0.002863,0.03426,0.006496,0.008842,-0.017839,-0.010597,0.003664,0.002254,0.009127,0.005068,0.004399,-0.003377,-0.000374,0.005564,-0.009244,0.002289,-0.010897
Verona_LIA:3227__BC_203__Cov_91.90%,0.134311,0.151314,0.043746,-0.002261,0.049855,-0.008367,0,0.001615,0.030474,0.036812,-0.003085,0.005695,-0.019029,0.002064,0.004479,0.00358,-0.000652,0.007855,0.013324,-0.000375,0.001747,0.00371,-0.006779,-0.006266,0.001916
Verona_LIA:3779__BC_200__Cov_23.92%,0.122929,0.149283,0.053551,0.00323,0.054164,-0.015618,0.00329,0.012461,0.02986,0.037723,-0.00065,0.014237,-0.025718,-0.017203,0.003122,0.00716,0.020861,0.005068,0.00264,-0.012256,-0.002371,0.013231,0.010599,-0.016629,-0.00012
Verona_LIA:3196__BC_200__Cov_92.57%,0.127482,0.151314,0.051666,-0.010013,0.058472,0,-0.00282,0.008077,0.016771,0.037541,-0.001624,0.004046,-0.020515,-0.012799,0.005565,0.00411,0.004042,-0.00038,0.003897,-0.006128,0.002121,0.007048,-0.007395,0.005061,0.00479
Verona_LIA:3225__BC_200__Cov_81.84%,0.114961,0.146236,0.047517,0.010659,0.044316,-0.000279,-0.00799,-0.007615,0.02168,0.026971,-0.000974,0.012139,-0.022002,-0.007707,0.008822,-0.011005,-0.007953,0.002914,0.006913,-0.003877,0.002496,0.004822,-0.007888,0.003494,-0.002994
Verona_LIA:3206__BC_200__Cov_81.03%,0.118376,0.147252,0.049403,0.012274,0.04924,0.000837,-0.00282,0.001846,0.019225,0.033714,-0.00065,0.001499,-0.02334,-0.009771,0.010043,-0.001724,-0.000391,0.003294,0.00817,-0.004252,-0.00574,-0.002968,0.001479,-0.003012,-0.003113
DolgeNjive_EIA.AG:I22934.AG__BC_675__Cov_11.83%,0.130897,0.155376,0.035449,0.01615,0.029852,-0.010319,0.011516,-0.002308,0.007363,0.029887,-0.001949,0.014387,-0.02111,-0.013625,0.00095,0.018297,0.004433,0.003674,-0.010433,-0.006128,0.006738,0.009892,0.001849,0.004699,-0.00455
Verona_LIA:3217__BC_200__Cov_90.30%,0.119514,0.151314,0.046763,0.001615,0.054472,-0.000558,-0.00329,0.004384,0.017385,0.036629,-0.004384,0.005245,-0.013825,-0.009771,-0.006515,-0.007955,-0.001173,0.0019,0.002011,-0.006628,-0.003369,0.003339,0.001232,-0.007591,-0.002515
TarquiniaMonterozzi_IA.SG:R10361.SG__BC_378__Cov_84.46%,0.12862,0.147252,0.045632,-0.000646,0.054472,-0.000837,0.004465,0.003692,0.018203,0.037905,-0.004872,0.008542,-0.020812,-0.013625,-0.002036,0.000796,0.001956,0.003421,0.00729,-0.01038,-0.002371,-0.003833,-0.006779,-0.001325,-0.007544
Etruria_Casenovole.AG:CSN008.AG__BC_400__Cov_19.90%,0.135449,0.150298,0.049403,0.006783,0.048932,0.004183,-0.001645,0.000923,0.016566,0.033167,-0.011205,0.003597,-0.020515,-0.017203,-0.001357,-0.007027,-0.008996,0.006081,0.006536,-0.002126,0.006863,0.004204,0.006286,-0.010001,-0.002275