Modern people of the Baltic nations whose ancestry is not recently admixed usually show over half of their autosomal dna ancestry is inheritied from Hunter & Gatherers of the region. The Lithuanian language preserves many archaic words, not only derived from the Corded Ware culture, but also presumably from the surviving Hunter & Gatherer populations which persisted up to the Bronze Age. An example of one would be "kasulas" - a hunting spear made of hazelwood. Germanic languages also have relic words from the Hunter & Gatherers. When the Uralics arrived later, they borrowed Corded Ware Baltic type words into their languages, as well as words from the Hunter & Gatherers who persisted. Petri Kallo estimated about 200 words, such as Finnish "halla" frost, from a Baltic language word "šalnas" - still current in modern Lithuanian. Acorns don't fall far from the Oak tree.
The mesolithic hunter-gatherer element of Lithuanian dna is already an admix of western hunter-gatherer and eastern hunter-gatherer. So it’s a toss-up what they spoke by the time neolithic farmers got there, let alone the steppe element. Potentially, archaic words could come from several different language groups.
That 50% hunter gatherer ancestry doesn’t need to be 50% from the Mesolithic, but result Mesolithic ancestry, plus that carried back in from groups which themselves had Euro hunter gatherer DNA (EEF minority, EHG/WSH majority)
They are related but it is not completely clear how. Some Bell Beakers seem to have spread from Spain along the coast north, but also inland in Europe along the rivers and from the Nederland area to Britain.