I think we have 2 ways to do that:

1. Update line item price: By this way, we need to do some below steps when validating cart:

• Run placed price processor to update latest price in case of changing price
• Calling Apply discounts for whole order
• Update placed price again based on comparing applied discount price to sale price. We only need to get discount amounts to compare, no need to run promotion anymore. However, we also need to clear applied discounts if we choose sale price instead of applying discount price  

2. Update discount amount: By this way, we won't change placed price in every line item. We will only re-update line item discount amount if discount amount > Max discount amount (Regular Price - Sale Price). Here is steps that we need to do when validating cart:

• Run placed price processor to update latest price in case of changing price
• Calling Apply discounts for whole order
• Comparing applied discount price to sale price. If Sale price is lower than discount price then update line item discount amount = Max discount amount (Regular Price - Sale Price). 

That is my ideas, the option 2 is more simple I think.

@Binh Nguyen: Thank you so much for the idea, I ended up creating a cart extension method to do the check and update the placed price. But it only works fine if I have a single SKU in the cart. Upon having more than 1 SKU it double discounts all line items other than the last one which is very strange.

            if (cart.GetFirstForm().Promotions.Any())
            {
                var currentMarket = ServiceLocator.Current.GetInstance<ICurrentMarket>().GetCurrentMarket();
                //Look for a line item promo
                PromotionInformation promo = cart.GetFirstForm().Promotions.Where(x => x.DiscountType == DiscountType.LineItem).FirstOrDefault();
                if (promo != null)
                {
                    //Create an in memory order group and see the discount
                    var inMemoryOrderGroup = new InMemoryOrderGroup(currentMarket, ServiceLocator.Current.GetInstance<CurrencyService>().GetCurrentCurrency().CurrencyCode);

                    foreach (ILineItem lineItem in cart.GetFirstForm().GetAllLineItems())
                    {
                        EntryContentBase entry = lineItem.GetEntryContent(ServiceLocator.Current.GetInstance<ReferenceConverter>(), ServiceLocator.Current.GetInstance<IContentLoader>());

                        decimal currentPlacedPrice = placedPriceUpdater.GetPlacedPrice(entry, lineItem.Quantity, ServiceLocator.Current.GetInstance<CurrentCustomerProfile>().GetCurrentCustomer(), currentMarket.MarketId, ServiceLocator.Current.GetInstance<CurrencyService>().GetCurrentCurrency()).Value.Amount;
                        //Passing regular price into the promotion engine
                        lineItem.PlacedPrice = Convert.ToDecimal(lineItem.Properties[Constants.Metadata.LineItem.ListPrice]);
                        inMemoryOrderGroup.AddLineItem(lineItem);

                        if (!string.IsNullOrEmpty(promo.CouponCode))
                        {
                            inMemoryOrderGroup.GetFirstForm().CouponCodes.Add(promo.CouponCode);
                        }

                        var rewards = ServiceLocator.Current.GetInstance<IPromotionEngine>().Run(inMemoryOrderGroup);

                        if (rewards.Any())
                        {
                            RewardDescription reward = rewards.OrderByDescending(x => x.SavedAmount).FirstOrDefault();
                            decimal promoFinalPrice = reward.Redemptions.FirstOrDefault().AffectedEntries.PriceEntries.Where(x => x.OriginalTotal == Convert.ToDecimal(lineItem.Properties[Constants.Metadata.LineItem.ListPrice])).FirstOrDefault().Price;


                            if (promoFinalPrice < currentPlacedPrice)
                            {
                                lineItem.PlacedPrice = Convert.ToDecimal(lineItem.Properties[Constants.Metadata.LineItem.ListPrice]);
                            }
                            else
                            {
                                lineItem.PlacedPrice = currentPlacedPrice;
                                lineItem.TrySetDiscountValue(x => x.EntryAmount, 0.0M);
                                var entryPromo = promo.Entries.Where(x => x.EntryCode == lineItem.Code).FirstOrDefault();
                                entryPromo.SavedAmount = 0.0M;
                            }
                        }
                        else
                        {
                            lineItem.PlacedPrice = currentPlacedPrice;
                        }
                    }
                }
                
            }

Here is an sample: https://www.screencast.com/t/ZMaw4YOJSj

The customer disocunt was 20% and the Epi coupon was 15%. In the image, you can see that all line items are being double discounted other than the last line item. I also had a look at the LineItem table and I see that LineItemDiscountAmount is populated with $6.66 for Item 1 and $4.32 for Item 2.

The problem here is you ran promotion in the loop. For every iterator, you added more 1 line item and get all discounts for all items in the memory order. So  the discounts retrieved may be not proper if you don't have all line items in the order. 

Binh Nguyen: Thank you so much! :)