Cubic spline fitting

If I have the following data:

lengthscale1SB = {{0, 3.3207054175811526`}, {0,      3.3400591587861697`}, {0, 3.233644563960887`}, {0,      3.2921487465109793`}, {0, 3.2469424529477506`}, {0, 3.21`}}; lengthscale2SB = {{100, 3.451567132493231`}, {100,      3.106439411731513`}, {100, 2.98780605221918`}, {100,      2.9436520687559216`}, {100, 3.015356426881061`}, {100,      2.921801274822571`}}; lengthscalemix1SB = {{79, 2.745901745363692`}, {79,      2.7224048172692563`}, {79, 2.598727747712638`}, {79,      2.495395024671054`}, {79, 2.4539983147912157`}, {79,      2.3661401389908012`}}; lengthscalemix2SB = {{30, 3.2164868427740267`}, {30,      3.2796631480447296`}, {30, 3.334462464220413`}, {30,      3.333075533653907`}, {30, 3.312618498873188`}, {30,      3.2523144754962625`}}; lengthscalemix3SB = {{45, 3.20562332399099`}, {45,      3.216687023360738`}, {45, 3.2134749616936547`}, {45,      3.1442955345260786`}, {45, 3.092326260475452`}, {45,      3.0565477670812813`}}; lengthscalemix4SB = {{88, 2.443872015229411`}, {88,      2.279005293131736`}, {88, 2.09077460471444`}, {88,      2.009572697828747`}, {88, 2.016343546704775`}, {88,      1.9602766903810653`}}; lengthscalemix5SB = {{15, 3.2976249123522816`}, {15,      3.3692960038716144`}, {15, 3.3543150770245402`}, {15,      3.3506633046912224`}, {15, 3.3408003286718615`}, {15,      3.2738395043851813`}}; 

How can I fit it to a cubic spline?

The idea is to try to fit or provide a guide to the eye line to that data perhaps similar to this:

enter image description here