The best replacement for lasso is ridge.

The best alternatives to lasso are rated as following:
★★★★★  ridge
★★★★★  stepwise
★★★★  lariat
★★★★  lars
★★★  stepwise regression
★★★  basis pursuit
★★  snare
  bunga citra lestari
  correa
  bunga cinta lestari

Your alternative for lasso is not listed? Suggest!
Speaking about lasso, one probably shouldn't forget about overlap and graph lasso.

Other search terms related to lasso and their ratings are:
★★★★★ overlap and graph lasso
You have in mind a companion for lasso and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of lasso in all years. Click on graph for more.
lasso
ridge
stepwise