They can add and amend, then it's sent back.
The gov can choose to accept the changes, or ping pong it and choose not.
At no point are the house of lord, lawmakers.
As you said they can amend,
It seems they can suggest, but they can't make laws.
Yes they can, bills can be started in HoL.
And no the government can’t simply ignore the HoL, remember our government doesn’t pass any laws, that is a power reserved for the two houses.
From Parliament’s own website “What the Lords does”
...snip... The Lords shares the task of making and shaping laws ...snip...