No, it’s a completely different word. Depending upon its context, it can have a range of meanings from ‘I can’t be sure about it, but X is probably the case’, ‘I wonder why X is the case’, ‘is it because of something that X is the case?’ or simply, ‘it probably is X’. 〜らし – the premodern equivalent of 〜らしい has a range of more definite meannings: ‘it certainly appears that X is the case’, ‘judging by appearance, I would presume that’, and so forth.
Is ~らむ an archaic or literary form of ~らしい, or something completely different?
No, it’s a completely different word. Depending upon its context, it can have a range of meanings from ‘I can’t be sure about it, but X is probably the case’, ‘I wonder why X is the case’, ‘is it because of something that X is the case?’ or simply, ‘it probably is X’. 〜らし – the premodern equivalent of 〜らしい has a range of more definite meannings: ‘it certainly appears that X is the case’, ‘judging by appearance, I would presume that’, and so forth.