Strictly speaking this should be 'She MAY give you a lift', (the full meaning is 'she is allowed to give you a lift)
In spoken English, definitely in the UK not sure about other places, 'May' has been replaced by 'Can' even though the meaning of 'can' is 'to be able' rather then being 'allowed to'.
She will give you a lift = Gwnaiff hi roi lifft i chi (SW) Mi wneith hi roi lifft i chi (NW).
She can give you a lift = Gall hi roi lifft i chi (SW), Mi all hi roi lifft i chi (NW)
Can we not also say "mae hi'n gallu rhoi lifft i chi", or is that less idiomatic?
Also, how would use may in the sense of "she might give you a lift"?
To express 'can' or 'to be able to'; you're correct.
'Mae hi'n gallu rhoi lifft i chi' (no mutation after gallu) is fine and understood but is a bit long winded and most advanced learners and native speakers would use the short form:-
'Gall hi roi lifft i chi' ('roi' is mutated because it is the 'object' of the short form verb)
To express a conditional form of 'can' or 'to be able' we use either the long form:-
Basai/Byddai hi'n rhoi lifft i chi = 'She (would be able/could) give you a lift
or the short form:-
Gallai hi roi lifft i chi
Since 'might' has different possible meanings the exact one you wanted would depend on context.
Gaiff hi roi lifft i chi (She might (as in 'may have permission') give you a lift)
Gall hi roi lifft i chi (She might (as in 'is able to') give you a lift)
Gallai hi roi lifft (She might (as in 'possibly could') give you a lift.
For 'might/may' in the sense of 'perhaps', efallai is a common word to use:
- Efallai bydd hi'n rhoi lifft i ti - Perhaps she will give you a lift
- Efallai basai hi'n rhoi lifft i ti - Perhaps she would give you a lift
efallai is often shortened to falle (and variations).
There are some other words and patterns that are used, too.