Philipe has answered, but I will expand on 2.
This is not an example of さえ ＋ Verb‐ば, here さえ is being used to add some extra nuance to 生きて. The ーて form of verbs and adjectives can be freely followed by the various markers は, も, さえ, など, なんか, ばかり, でも, しか, こそ, のみ, すら to add focus, restriction, emphasis etc. Some examples:
あなたのご親切に頼ってしか生きていけない Only by relying on your kindness can I live on.
法は大多数の人に守られてこそ法の価値がある Law has its value precisely because it is upheld by the majority of people.
それだけの金をかけてまでなぜ難工事のトンネルを掘らねばならないのか Why is it that they have to go to the extent of spending so much money to build a difficult-to-engineer tunnel?
Some examples with ーている:
運動しないで寝てばかりいた身には風呂は応えた His body, having done nothing but lie around without exercise, felt the effect of the hot bath.
起きてだけはいますがまだ歩けません I am on my feet, at least, but I still can't walk.
As discussed elsewhere (here), one meaning of さえ is 'only, just', so the quoted sentence in your example sentence means
'if you [do me the favour of] only/just staying alive/continuing to live'
In the ーたらと思っていた construction, いい has been elided after ーたら, ーたらいい
being a common way to express a hope or wish, 'I wished/hoped that you would keep living/stay alive for me...'.