You have to think carefully about "importance" of selected predictors and what "p-values" really mean in LASSO.
Demonstrations of LASSO can be based on a simulated data set with a small number of predictors associated with outcome and a large number that are not. In that context it works well to find the truly important predictors.
But in real-world applications, with multiple predictors that are correlated with each other, the choice of "important" predictors will vary from sample to sample from the same population. The variability in "importance" among predictors you saw among re-samples of your data, and that forms the basis of the stability selection method recommended in the answer by @Edgar, should lead to some questions about what "importance" of individual predictors means when there are multiple correlated predictors related to outcome.
Even when LASSO returns a value of 0 for a predictor's coefficient (as it is designed to do), that doesn't mean it's "not meaningful"; it just means that it didn't add enough to the model to matter for your particular sample and sample size. The predictors that were selected might be important within your particular data sample, but that doesn't mean they are the most important in any fundamental sense in the overall population and they certainly can't be interpreted to have causal effects on outcome.
Your particular approach based on ranking of coefficient values is potentially dangerous, depending on how it is done. Predictors are typically standardized before LASSO so that differences in measurement scales don't differentially affect the penalization of the coefficients. But some software then re-scales the coefficients to the original measurement scales. So at the least you have to be careful about whether you are ranking coefficients for standardized or for re-scaled predictors. You don't want the importance of a predictor having a length value to differ depending on whether you measured it in millimeters or miles.
In many applications, the most important issue with LASSO is how well the model works for prediction. A strength of LASSO is that, even with its potentially unstable selection among correlated predictors, models can work quite well in practice for prediction. In that context, p-values for individual coefficients are of little interest.
It's when you are interested in inference that p-values matter. This is a very difficult problem in LASSO or in any modeling approach that uses outcomes to select predictors. The usual assumptions for estimating p-values in standard regression models no longer hold when you have used the outcomes to select predictors. There has been some work on this in recent years, introduced for example in Chapters 16 and 20 of Computer Age Statistical Inference. Under some assumptions it is possible to estimate p-values, but I think that it's safe to say this is still an area of active research interest. Unless you are willing to get into these issues in depth, it might be best to stay away from p-values for individual coefficients in LASSO.