Firstly we're a long way off from this being anything close to a reality, let's have a successful implementation of the LN before we start considering replacing existing alts. I don't think anyway it would replace them, some alts have real uses with great people behind them, you can't replace that.
Yes. The Lightning Network would need to become successful for sidechains to operate as intended in the future. Even though sidechains will exist, I believe that they might not completely replace altcoins since each altcoin has its unique features and use cases. If a sidechain would be implemented for each unique feature that an altcoin has, it would take a lot of effort. That's why, altcoins could co-exist with sidechains for years to come, as people would have the choice to operate within the Bitcoin network or an independent blockchain from an altcoin.
However, if sidechains become useful and extremely popular, then people might use them more than altcoins themselves. Bitcoin would become an "All-in-one" cryptocurrency capable of providing a wealth of blockchain services we know and love today. The most interesting sidechain yet, would be Rootstock as it'll become a fierce competitor against Ethereum, EOS, Cardano, NEO and other smart contract platforms in the market today.
Therefore, it's only a matter of time before Lightning Network becomes stable and widely used in the mainstream world to open the path for sidechains and other improvements within the Bitcoin network. By then, the market and the people will decide whenever they'll continue to use altcoins or sidechains instead. Just my opinion
