Actually glycogen reserves are about 60% of normal while on LC. I believe this is Lyle McDonald. My normal HIIT for 30min is no problem on higher carbs but on LC 15min is disastrous.
There are some changes that take a month but really your muscles should be fueled by ketones and gluconeogeneisis by day 2.
Lifting heavy is fine just increase your time between sets. I ended up moving to a 3 day split so I could keep it under 45 minutes a session unless its high volume low intensity like shoulders and upper back.