I think that Biden's handlers are making socio-political hay out of next to nothing.
Fact: "Lake City" is officially the Lake City Army Ammunition Plant, a govt owned facility operated previously by Orbital/ATK and now the new contract was let to Winchester Ammunition to operate the plant. The new contract was let because LCAAP is mostly converting to the new 6.8mm round being adopted by the Army. The 5.56 lines they are keeping in production are going to support legacy needs during the transition phase and also shipments of 5.56 to Ukraine, but the bulk of the facility's production moving forward will be 6.8.
The LC 5.56 / 223 that has been made available to the US general public has been essentially "seconds" and blems. Now that production of 5.56 is being reduced, it follows that whatever 5.56/223 seconds/blems that normally were sold commercially to Americans in the interests of recouping material and manufacturing costs will also be reduced in quantity. Also, it is highly likely that any seconds or blems will be channeled to Ukraine.
The upshot of the conversion of LCAAP to 6.8 is, you can't sell commercially to the US public what you don't have available to sell. If you're string-pulling liberal puppetmasters in .gov service, you realize this and write a speech for Biden to deliver that is certain to increase upward pricing pressure on what 5.56/223 IS available, given that the Ukraine conflict has sucked up any Russian/Ukranian sourced of Wolf/Tula etc. steel case. That "No more LC ammo, folks" speech's expected effect on pricing will make it even more economically difficult for Americans to find and purchase 5.56/223, which works in the best interests of liberal puppetmasters to limit firearms purchase and use in the US.
Essentially, politicians being politicians: Telling the truth but not the whole truth in their own self-serving interests, at Americans' expense.